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Two-weighted inequalities for integral operators in \(L_p\)-spaces of Banach-valued functions and their applications. (English. Russian original) Zbl 1090.46029

Function spaces, approximations, and differential equations. Collected papers dedicated to Oleg Vladimirovich Besov on his 70th birthday. Transl. from the Russian. Moscow: Maik Nauka/Interperiodika. Proceedings of the Steklov Institute of Mathematics 243, 185-203 (2003); translation from Tr. Mat. Inst. Steklova 243, 194-212 (2003).
Summary: In the spaces \(L_p(\Omega_k,B)\), strong- and weak-type two-weight inequalities are obtained for integral operators arising from the Il’in-Besov integral representation in the case of radial weights.
For the entire collection see [Zbl 1064.46002].

MSC:

46E40 Spaces of vector- and operator-valued functions
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47G10 Integral operators
26D10 Inequalities involving derivatives and differential and integral operators
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