Weighted inequalities for higher dimensional one-sided Hardy-Littlewood maximal function in Orlicz spaces

2021 ◽  
Author(s):  
Abhishek Ghosh ◽  
Parasar Mohanty
Keyword(s):  
Maximal Function ◽  
Orlicz Spaces ◽  
Weighted Inequalities ◽  
Littlewood Maximal Function ◽  
Higher Dimensional

scholarly journals A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Alberto Fiorenza
Keyword(s):  
Bounded Domain ◽  
Maximal Function ◽  
Orlicz Spaces ◽  
Local Estimate ◽  
Lebesgue Spaces ◽  
Littlewood Maximal Function

It is proven that if1≤p(·)<∞in a bounded domainΩ⊂Rnand ifp(·)∈EXPa(Ω)for somea>0, then givenf∈Lp(·)(Ω), the Hardy-Littlewood maximal function off,Mf, is such thatp(·)log(Mf)∈EXPa/(a+1)(Ω). Becausea/(a+1)<1, the thesis is slightly weaker than(Mf)λp(·)∈L1(Ω)for someλ>0. The assumption thatp(·)∈EXPa(Ω)for somea>0is proven to be optimal in the framework of the Orlicz spaces to obtainp(·)log(Mf)in the same class of spaces.

Weighted Inequalities in Lorentz and Orlicz Spaces

10.1142/1367 ◽  
1991 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Miroslav Krbec
Keyword(s):  
Orlicz Spaces ◽  
Weighted Inequalities

The Hardy–Littlewood maximal function

2014 ◽  
pp. 187-188
Author(s):  
Omar El-Fallah ◽  
Karim Kellay ◽  
Javad Mashreghi ◽  
Thomas Ransford
Keyword(s):  
Maximal Function ◽  
Littlewood Maximal Function

scholarly journals A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function

2002 ◽  
Vol 65 (2) ◽  
pp. 253-258 ◽  
Author(s):  
Hitoshi Tanaka
Keyword(s):  
Sobolev Space ◽  
Maximal Function ◽  
60Th Birthday ◽  
One Dimensional ◽  
Partial Derivatives ◽  
First Order ◽  
Littlewood Maximal Function ◽  
The One ◽  
Derivatives Of

Dedicated to Professor Kôzô Yabuta on the occasion of his 60th birthdayJ. Kinnunen proved that of P > 1, d ≤ 1 and f is a function in the Sobolev space W1,P(Rd), then the first order weak partial derivatives of the Hardy-Littlewood maximal function ℳf belong to LP(Rd). We shall show that, when d = 1, Kinnunen's result can be extended to the case where P = 1.

Sign in / Sign up

Export Citation Format

Share Document