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Eurasian Mathematical Journal, 2018, Volume 9, Number 2, Pages 82–88
(Mi emj299)
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This article is cited in 6 scientific papers (total in 6 papers)
Short communications
Marcinkiewicz-type interpolation theorem and estimates for convolutions for Morrey-type spaces
V. I. Burenkovab, D. K. Chigambayevac, E. D. Nursultanovd a Cardiff School of Mathematics,
Cardiff University
Senghennydd Rd,
Cardiff CF24 4AG, UK
b S.M. Nikol'skii Mathematical Institute,
RUDN University,
6 Miklukho-Maklay St, 117198, Moscow, Russia
c L.N. Gumilyov Eurasian National University,
2 Satpayev St, 010008, Astana, Kazakhstan
d Lomonosov Moscow State University, Kazakhstan branch,
11 Kazhimukan St, 010010, Astana, Kazakhstan
Abstract:
We introduce a class of Morrey-type spaces $M_{p,q,\Omega}^\lambda$, which includes the classical Morrey spaces. We discuss their properties and we prove a Marcinkiewicz-type interpolation theorem. This theorem is then applied to obtaining a Young–O'Neil-type inequality for the convolution operator in Morrey-type spaces.
Keywords and phrases:
Morrey spaces, generalized Morrey-type spaces, interpolation theorem, convolution operator.
Received: 01.08.2017
Citation:
V. I. Burenkov, D. K. Chigambayeva, E. D. Nursultanov, “Marcinkiewicz-type interpolation theorem and estimates for convolutions for Morrey-type spaces”, Eurasian Math. J., 9:2 (2018), 82–88
Linking options:
https://www.mathnet.ru/eng/emj299 https://www.mathnet.ru/eng/emj/v9/i2/p82
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Abstract page: | 436 | Full-text PDF : | 190 | References: | 48 |
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