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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 Kαf(x,t)=∫|y|≤2|x|(|x−y|+t)α−nf(y)dy, t∈[0,∞), x∈Rn, that acts from Lp(Rn) to Lqν(Rn+1+), where 1<p<∞, 0<q<∞, α>n/p, and ν is a positive Borel measure on Rn+1+. Also, two-sided estimates for a measure of noncompactness of the operator Kα 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: | 373 | Full-text PDF : | 119 | References: | 65 |
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