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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2001, Volume 232, Pages 164–178
(Mi tm211)
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Boundedness and Compactness Criteria for a Generalized Truncated Potential
V. M. Kokilashvili A. Razmadze Mathematical Institute, Georgian Academy of Sciences
Abstract:
Boundedness and compactness criteria are established for a generalized truncated Riesz potential $K_{\alpha} f(x,t) =\int _{|y|\leq 2|x|} (|x-y| +t)^{\alpha -n} f(y)\,dy$, $t\in [0,\infty)$, $x\in \mathbb R^n$, that acts from $L^p (\mathbb R^n)$ to $L_{\nu }^q (\mathbb R_+^{n+1})$, where ${1<p<\infty }$, ${0<q<\infty}$, ${\alpha >n/p}$, and $\nu$ is a positive Borel measure on $\mathbb R_+^{n+1}$. Also, two-sided estimates for a measure of noncompactness of the operator $K_{\alpha }$ are obtained.
Received in July 2000
Citation:
V. M. Kokilashvili, “Boundedness and Compactness Criteria for a Generalized Truncated Potential”, Function spaces, harmonic analysis, and differential equations, Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 232, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 164–178; Proc. Steklov Inst. Math., 232 (2001), 157–171
Linking options:
https://www.mathnet.ru/eng/tm211 https://www.mathnet.ru/eng/tm/v232/p164
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Abstract page: | 314 | Full-text PDF : | 93 | References: | 44 |
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