Generalized fractional maximal operator on generalized local Morrey spaces

Yıl 2020, Cilt: 69 Sayı: 1, 73 - 87, 30.06.2020

Abdulhamit Küçükaslan Vagif S. Guliyev Ayhan Serbetci

https://doi.org/10.31801/cfsuasmas.508702

Cited By: 5

Öz

In this paper, we study the boundedness of generalized fractional maximal operator  on generalized local Morrey spaces and

generalized Morrey spaces, including weak estimates. Firstly, we prove the Spanne type boundedness of generalized fractional maximal operator  on generalized local Morrey spaces for 1 < p < q < infinity and, on weak generalized local Morrey spaces for p = 1 and 1 < q < infinity. Secondly, we prove the Adams type boundedness of generalized fractional maximal operator  on generalized local Morrey spaces for 1<p<q< \infinity   

and, on  weak generalized local Morrey spaces for p = 1 and 1 < q < \infinity. In all cases the conditions for the boundedness of generalized fractional maximal operators are given in terms of supremal-type integral inequalities on (\varphi_1; \varphi_2; \rho) and (\varphi; \rho), which do not assume any assumption on monotonicity of \varphi_1(x; r), \varphi_2(x; r) and \varphi(x; r) in r.

Anahtar Kelimeler

Generalized fractional maximal operator, generalized local Morrey spaces, generalized Morrey spaces

Kaynakça

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