Marcinkiewicz-type interpolation theorem for Morrey-type spaces and its corollaries

2019

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DOI 10.1080/17476933.2019.1664488
Data confidence 70 medium
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Abstract

We introduce a class of Morrey-type spaces Mp,q,Ωλ, 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.