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Eurasian Math. J., 2018, Volume 9, Number 2, Pages 82–88 (Mi emj299)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00450_
Ministry of Education and Science of the Russian Federation
This work was supported by the Programme ``5-100'' of the Ministry of Education and Science of the Russian Federation and the Russian Foundation for Basic Research (project 16-01-00450).


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MSC: 42B35, 46E30, 46B70, 47B38, 47G10
Received: 01.08.2017
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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

Citation in format AMSBIB
\Bibitem{BurChiNur18}
\by V.~I.~Burenkov, D.~K.~Chigambayeva, E.~D.~Nursultanov
\paper Marcinkiewicz-type interpolation theorem and estimates for convolutions for Morrey-type spaces
\jour Eurasian Math. J.
\yr 2018
\vol 9
\issue 2
\pages 82--88
\mathnet{http://mi.mathnet.ru/emj299}


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