scholarly journals The maximal operator on generalized Orlicz spaces

2015 ◽  
Vol 269 (12) ◽  
pp. 4038-4048 ◽  
Author(s):  
Peter A. Hästö
Keyword(s):  
Maximal Operator ◽  
Orlicz Spaces

Commutators of Fractional Maximal Operator on Orlicz Spaces

2018 ◽  
Vol 104 (3-4) ◽  
pp. 498-507
Author(s):  
V. S. Guliyev ◽  
F. Deringoz ◽  
S. G. Hasanov
Keyword(s):  
Maximal Operator ◽  
Orlicz Spaces ◽  
Fractional Maximal Operator

The Maximal Operator in Variable Spaces 𝐿 𝑝(·)(Ω, ρ) with Oscillating Weights

2006 ◽  
Vol 13 (1) ◽  
pp. 109-125 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Natasha Samko ◽  
Stefan Samko
Keyword(s):  
Lipschitz Condition ◽  
Maximal Operator ◽  
Orlicz Spaces ◽  
Weight Functions ◽  
Power Functions ◽  
Index Numbers ◽  
Boyd Indices ◽  
Open Set ◽  
Class Weight ◽  
Young Functions

Abstract We study the boundedness of the maximal operator in the spaces 𝐿 𝑝(·)(Ω, ρ) over a bounded open set Ω in 𝑅𝑛 with the weight , where 𝑤𝑘 has the property that belongs to a certain Zygmund-type class. Weight functions 𝑤𝑘 may oscillate between two power functions with different exponents. It is assumed that the exponent 𝑝(𝑥) satisfies the Dini–Lipschitz condition. The final statement on the boundedness is given in terms of index numbers of functions 𝑤𝑘 (similar in a certain sense to the Boyd indices for the Young functions defining Orlicz spaces).

Sign in / Sign up

Export Citation Format

Share Document