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This article is cited in 3 scientific papers (total in 3 papers)
Marcinkiewicz-type interpolation theorem for Morrey-type spaces and its corollaries
V. I. Burenkovab, D. K. Chigambaevac, E. D. Nursultanovde a V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, Moscow, Russian Federation
b S. M. Nikol'skii Institute of Mathematics, RUDN University, Moscow, Russian Federation
c School of Mechanics and Mathematics, L. N. Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan
d Department of Mathematics, M. V. Lomonosov Moscow State University (Kazakhstan Branch), Nur-Sultan, Kazakhstan
e Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Abstract:
We introduce a class of Morrey-type spaces $M^\lambda_{p,q,\Omega}$, which includes the classical Morrey spaces and discuss their properties. We prove a Marcinkiewicz-type interpolation theorem for such spaces. This theorem is then applied to obtaining an analogue of O'Neil's inequality for convolutions and to proving the boundedness in the introduced Morrey-type spaces of the Riesz potential and singular integral operators.
Received: 04.07.2019 Accepted: 29.08.2019
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