{"id":41131,"date":"2024-09-26T06:46:25","date_gmt":"2024-09-26T06:46:25","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%a7%d9%86\/"},"modified":"2024-09-26T06:46:54","modified_gmt":"2024-09-26T06:46:54","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%a7%d9%86","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%a7%d9%86\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u062a\u06af\u0631\u0627\u0644 \u0647\u0627\u06cc \u0645\u0641\u0631\u062f \u062f\u0631 $ax+b$ \u0627\u0628\u0631\u06af\u0631\u0648\u0647 \u0647\u0627 \u0648 \u06cc\u06a9 \u0642\u0636\u06cc\u0647 \u0686\u0646\u062f \u0628\u0631\u0627\u0628\u0631 \u0637\u06cc\u0641\u06cc \u0628\u0627 \u0627\u0631\u0632\u0634 \u0639\u0645\u0644\u06af\u0631"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nSingular integrals on $ax+b$ hypergroups and an operator-valued spectral multiplier theorem<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u062a\u06af\u0631\u0627\u0644 \u0647\u0627\u06cc \u0645\u0641\u0631\u062f \u062f\u0631 $ax+b$ \u0627\u0628\u0631\u06af\u0631\u0648\u0647 \u0647\u0627 \u0648 \u06cc\u06a9 \u0642\u0636\u06cc\u0647 \u0686\u0646\u062f \u0628\u0631\u0627\u0628\u0631 \u0637\u06cc\u0641\u06cc \u0628\u0627 \u0627\u0631\u0632\u0634 \u0639\u0645\u0644\u06af\u0631<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nAlessio Martini, Pawe\u0142 Plewa<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n64<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nFunctional Analysis,Classical Analysis and ODEs,\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0639\u0645\u0644\u06a9\u0631\u062f\u06cc , \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u0648 ODE \u0647\u0627 ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 19 September, 2024; originally announced September 2024. , Comments: 64 pages , MSC Class: 42B15; 42B20; 43A22; 43A62<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 \u0634\u062f\u0647 \u062f\u0631 19 \u0633\u067e\u062a\u0627\u0645\u0628\u0631 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u062f\u0631 \u0633\u067e\u062a\u0627\u0645\u0628\u0631 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f. \u060c \u0646\u0638\u0631\u0627\u062a: 64 \u0635\u0641\u062d\u0647 \u060c \u06a9\u0644\u0627\u0633 MSC: 42B15 \u061b42b20 \u061b43a22 \u061b43A62<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
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\n Semantic Scholar<\/a>
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\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

Let $L_\u03bd= -\\partial_x^2-(\u03bd-1)x^{-1} \\partial_x$ be the Bessel operator on the half-line $X_\u03bd= [0,\\infty)$ with measure $x^{\u03bd-1} \\,\\mathrm{d} x$. In this work we study singular integral operators associated with the Laplacian $\u0394_\u03bd= -\\partial_u^2 + e^{2u} L_\u03bd$ on the product $G_\u03bd$ of $X_\u03bd$ and the real line with measure $\\mathrm{d} u$. For any $\u03bd\\geq 1$, the Laplacian $\u0394_\u03bd$ is left-invariant with respect to a noncommutative hypergroup structure on $G_\u03bd$, which can be thought of as a fractional-dimension counterpart to $ax+b$ groups. In particular, equipped with the Riemannian distance associated with $\u0394_\u03bd$, the metric-measure space $G_\u03bd$ has exponential volume growth. We prove a sharp $L^p$ spectral multiplier theorem of Mihlin–H\u00f6rmander type for $\u0394_\u03bd$, as well as the $L^p$-boundedness for $p \\in (1,\\infty)$ of the associated first-order Riesz transforms. To this purpose, we develop a Calder\u00f3n–Zygmund theory \u00e0 la Hebisch–Steger adapted to the nondoubling structure of $G_\u03bd$, and establish large-time gradient heat kernel estimates for $\u0394_\u03bd$. In addition, the Riesz transform bounds for $p > 2$ hinge on an operator-valued spectral multiplier theorem, which we prove in greater generality and may be of independent interest.<\/p>\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u0628\u06af\u0630\u0627\u0631\u06cc\u062f $ l_\u03bd =-\\ partial_x^2- (\u03bd-1) x^{-1} \\ partial_x $ \u0627\u067e\u0631\u0627\u062a\u0648\u0631 BESSEL \u062f\u0631 \u0646\u06cc\u0645\u0647 \u062e\u0637 $ x_\u03bd = [0 \u060c \\ infty) $ \u0628\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc $ x^{\u03bd \u03bd-1} \\ \u060c \\ mathrm {d} x $.\u062f\u0631 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u060c \u0645\u0627 \u0627\u067e\u0631\u0627\u062a\u0648\u0631\u0647\u0627\u06cc \u0627\u0646\u062a\u06af\u0631\u0627\u0644 \u0645\u0641\u0631\u062f \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 \u0644\u0627\u067e\u0644\u0627\u0633\u06cc $ \u0394_\u03bd = -\\ partial_u^2 + e^{2u} l_\u03bd $ \u0631\u0627 \u062f\u0631 \u0645\u062d\u0635\u0648\u0644 $ g_\u03bd $ \u0627\u0632 $ x_\u03bd $ \u0648 \u062e\u0637 \u0648\u0627\u0642\u0639\u06cc \u0628\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 $ \\ mathrm {d} \u0645\u0637\u0627\u0644\u0639\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.u $\u0628\u0631\u0627\u06cc \u0647\u0631 $ \u03bd \\ geq 1 $ \u060c Laplacian $ \u0394_\u03bd $ \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u06cc\u06a9 \u0633\u0627\u062e\u062a\u0627\u0631 \u0628\u06cc\u0634 \u0627\u0632 \u062d\u062f \u063a\u06cc\u0631 \u06af\u0631\u0648\u0647\u06cc \u062f\u0631 $ g_\u03bd $ \u060c \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0647\u0645\u062a\u0627\u06cc \u0628\u0639\u062f\u06cc \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \u0628\u0647 \u06af\u0631\u0648\u0647 \u0647\u0627\u06cc AX+B $ \u0641\u06a9\u0631 \u06a9\u0631\u062f \u060c \u0645\u062a\u063a\u06cc\u0631 \u0627\u0633\u062a.\u0628\u0647 \u0637\u0648\u0631 \u062e\u0627\u0635 \u060c \u0645\u062c\u0647\u0632 \u0628\u0647 \u0641\u0627\u0635\u0644\u0647 \u0631\u06cc\u0645\u0627\u0646\u06cc\u0627\u0646 \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 $ \u0394_\u03bd $ \u060c \u0641\u0636\u0627\u06cc \u0645\u062a\u0631\u06cc\u06a9 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc $ g_\u03bd $ \u062f\u0627\u0631\u0627\u06cc \u0631\u0634\u062f \u062d\u062c\u0645 \u0646\u0645\u0627\u06cc\u06cc \u0627\u0633\u062a.\u0645\u0627 \u06cc\u06a9 \u0642\u0636\u06cc\u0647 \u062a\u06cc\u0632 $ l^p $ mileplier mihlin-\u0646\u0648\u0639 H\u00f6rmander \u0628\u0631\u0627\u06cc $ \u03b4_\u03bd $ \u060c \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 $ l^p $ -Boundedness \u0628\u0631\u0627\u06cc $ p \\ in (1 \u060c \\ infty) $ \u0627\u0648\u0644 \u0627\u0632 \u0645\u0631\u062a\u0628\u0637 \u0631\u0627 \u0627\u062b\u0628\u0627\u062a \u0645\u06cc \u06a9\u0646\u06cc\u0645.-\u0631\u062f Riesz \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u0634\u0648\u062f.\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0646\u0638\u0648\u0631 \u060c \u0645\u0627 \u06cc\u06a9 \u062a\u0626\u0648\u0631\u06cc Calder\u00f3n-zhegmund \u00e0 la Hebisch-Steger \u0633\u0627\u0632\u06af\u0627\u0631 \u0628\u0627 \u0633\u0627\u062e\u062a\u0627\u0631 \u063a\u06cc\u0631 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 $ g_\u03bd $ \u060c \u0648 \u0628\u0631\u0622\u0648\u0631\u062f \u0647\u0633\u062a\u0647 \u06af\u0631\u0645\u0627\u06cc \u0634\u06cc\u0628 \u0628\u0632\u0631\u06af \u0631\u0627 \u0628\u0631\u0627\u06cc $ \u03b4_\u03bd $ \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u06cc\u0645.\u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646 \u060c \u0645\u0631\u0632\u0647\u0627\u06cc \u062a\u0628\u062f\u06cc\u0644 RIESZ \u0628\u0631\u0627\u06cc P> 2 $ $ \u0628\u0647 \u06cc\u06a9 \u0642\u0636\u06cc\u0647 \u0636\u0631\u0628 \u0637\u06cc\u0641\u06cc \u0628\u0627 \u0627\u0631\u0632\u0634 \u0627\u067e\u0631\u0627\u062a\u0648\u0631 \u060c \u06a9\u0647 \u0645\u0627 \u062f\u0631 \u06a9\u0644\u06cc\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u062b\u0628\u0627\u062a \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0645\u0648\u0631\u062f \u0639\u0644\u0627\u0642\u0647 \u0645\u0633\u062a\u0642\u0644 \u0628\u0627\u0634\u062f.<\/p>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n","protected":false},"excerpt":{"rendered":"

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