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Complex Variables and Elliptic Equations. An International Journal, 2020, Volume 65, Issue 1, Pages 87–108
DOI: https://doi.org/10.1080/17476933.2019.1664488 (Mi cvee5) 		 
This article is cited in 4 scientific papers (total in 4 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
Full-text PDF Citations (4)
DOI: https://doi.org/10.1080/17476933.2019.1664488
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.
Funding agency Grant number
Russian Science Foundation 19-11-00087
Ministry of Education and Science of the Russian Federation
Ministry of Education and Science of the Republic of Kazakhstan AP051 32071
AP051 32590
The research of V.I. Burenkov, Sections 1–3, was supported by the Russian Science Foundation (project no. 19-11-00087) and was carried out in the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences. His research, Sections 4 and 5, has been carried out with the support of the ‘RUDN University Program 5–100’ and was carried out in the S.M. Nikol'skii Mathematical Institute at the RUDN University. The research of E.D. Nursultanov was supported by the Ministry of Education and Science of the Republic of Kazakhstan (projects no. AP051 32071 and AP051 32590).
Received: 04.07.2019
Accepted: 29.08.2019
Bibliographic databases:
Document Type: Article
MSC: 42B35, 47B06, 47B38, 46B70, 47G10
Language: English
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