This article is cited in 6 papers

Short communications

Marcinkiewicz-type interpolation theorem and estimates for convolutions for Morrey-type spaces

V. I. Burenkov^ab, D. K. Chigambayeva^c, E. D. Nursultanov<sup>d

a</sup> 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.

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

Received: 01.08.2017

Language: English