Generalized fractional maximal operator on generalized local Morrey spaces

Authors : Abdulhamit KÜÇÜKASLAN, Vagif S. GULİYEV, Ayhan SERBETCİ

Pages : 73-87

Doi:10.31801/cfsuasmas.508702

View : 6 | Download : 9

Publication Date : 2020-06-30

Article Type : Research Paper

Abstract :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 insert ignore into journalissuearticles values(\varphi_1;  \varphi_ 2; \rho); and insert ignore into journalissuearticles values( \varphi ; \rho);, which do not assume any  assumption on monotonicity of  \varphi_ 1insert ignore into journalissuearticles values(x; r);,  \varphi_ 2insert ignore into journalissuearticles values(x; r); and  \varphi insert ignore into journalissuearticles values(x; r); in r.
Keywords : Generalized fractional maximal operator, generalized local Morrey spaces, generalized Morrey spaces