Abstract
The present article discusses the boundedness criteria for the fractional Hardy operators on weighted variable exponent Morrey–Herz spaces {Mdot{K}^{alpha(cdot),lambda}_{q,p(cdot)}(w)}.
Highlights
In mathematical analysis, the Hardy operator is considered a significant averaging operator and has been exercised a lot during the recent past
Recent advancements in the field of variable exponent function spaces include the development of its weighted theory based on the Muckenhoupt weights [30]
Izuki and Noi defined the weighted Herz spaces with variable exponents in [34]
Summary
The Hardy operator is considered a significant averaging operator and has been exercised a lot during the recent past. Hardy-type operators on different function spaces which include [5,6,7,8,9,10]. Recent advancements in the field of variable exponent function spaces include the development of its weighted theory based on the Muckenhoupt weights [30]. Izuki and Noi defined the weighted Herz spaces with variable exponents in [34]. Weighted Morrey–Herz spaces with variable exponents were defined and studied in [35, 36]. The aim of this article is to study the continuity criteria for fractional type Hardy operators on weighted variable exponents Morrey–Herz spaces. On the weighted Herz spaces, the boundedness of fractional integral operator was obtained by Izuki and Noi [34].
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