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

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.

Variable Exponent Lebesgue Spaces and Hardy-Littlewood Maximal Function on p-Adic Numbers

P-Adic Numbers Ultrametric Analysis and Applications ◽

10.1134/s2070046620020028 ◽

2020 ◽

Vol 12 (2) ◽

pp. 90-111

Author(s):

Leonardo Fabio Chacón-Cortés ◽

Humberto Rafeiro

Keyword(s):

Maximal Function ◽

Variable Exponent ◽

Lebesgue Spaces ◽

Variable Exponent Lebesgue Spaces

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

Expositiones Mathematicae ◽

10.1016/j.exmath.2021.07.005 ◽

2021 ◽

Author(s):

Abhishek Ghosh ◽

Parasar Mohanty

Keyword(s):

Maximal Function ◽

Orlicz Spaces ◽

Weighted Inequalities ◽

Higher Dimensional

Maximal function on Musielak–Orlicz spaces and generalized Lebesgue spaces

Bulletin des Sciences Mathématiques ◽

10.1016/j.bulsci.2003.10.003 ◽

2005 ◽

Vol 129 (8) ◽

pp. 657-700 ◽

Cited By ~ 139

Author(s):

Lars Diening

Keyword(s):

Maximal Function ◽

Orlicz Spaces ◽

Lebesgue Spaces

Variation Inequality for the Two-Dimensional Discrete Hardy–Littlewood Maximal Function

Results in Mathematics ◽

10.1007/s00025-021-01486-3 ◽

2021 ◽

Vol 76 (4) ◽

Author(s):

Fayou Zhao ◽

Hongxiu Zhou

Keyword(s):

Maximal Function ◽

Two Dimensional ◽

Variation Inequality

Weighted inequalities for the two-dimensional one-sided Hardy-Littlewood maximal function

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-2010-05343-7 ◽

2011 ◽

Vol 363 (04) ◽

pp. 1699-1699 ◽

Cited By ~ 7

Author(s):

L. Forzani ◽

F. J. Martín-Reyes ◽

S. Ombrosi

Keyword(s):

Maximal Function ◽

Two Dimensional ◽

Weighted Inequalities ◽

Application of the Hardy–Littlewood maximal function

Introduction toHpSpaces ◽

10.1017/cbo9780511470950.010 ◽

2009 ◽

pp. 170-199

Author(s):

Paul Koosis

Keyword(s):

Maximal Function ◽

THE HARDY-LITTLEWOOD MAXIMAL FUNCTION AND SOME OF ITS VARIANTS

Advanced Courses of Mathematical Analysis II ◽

10.1142/9789812708441_0003 ◽

2007 ◽

Cited By ~ 1

Author(s):

JAVIER DUOANDIKOETXEA

Keyword(s):

Maximal Function ◽

On the radial maximal function and the Hardy Littlewood maximal function in wedges

The Madison Symposium on Complex Analysis - Contemporary Mathematics ◽

10.1090/conm/137/1190998 ◽

1992 ◽

pp. 383-398 ◽

Cited By ~ 2

Author(s):

Jean-Pierre Rosay

Keyword(s):

Maximal Function ◽

Radial Maximal Function

The Hardy–Littlewood maximal function

A Primer on the Dirichlet Space ◽

10.1017/cbo9781107239425.012 ◽

2014 ◽

pp. 187-188

Author(s):

Omar El-Fallah ◽

Karim Kellay ◽

Javad Mashreghi ◽

Thomas Ransford

Keyword(s):

Maximal Function ◽

NONTRIVIAL SOLUTIONS FOR N-LAPLACIAN EQUATIONS WITH SUB-EXPONENTIAL GROWTH

Analysis and Applications ◽

10.1142/s021953051350005x ◽

2013 ◽

Vol 11 (03) ◽

pp. 1350005 ◽

Cited By ~ 1

Author(s):

ZHONG TAN ◽

FEI FANG

Keyword(s):

Dirichlet Problem ◽

Bounded Domain ◽

Exponential Growth ◽

Morse Theory ◽

Smooth Boundary ◽

Orlicz Spaces ◽

Nontrivial Solutions ◽

Laplacian Equations

Let Ω be a bounded domain in RNwith smooth boundary ∂Ω. In this paper, the following Dirichlet problem for N-Laplacian equations (N > 1) are considered: [Formula: see text] We assume that the nonlinearity f(x, t) is sub-exponential growth. In fact, we will prove the mapping f(x, ⋅): LA(Ω) ↦ LÃ(Ω) is continuous, where LA(Ω) and LÃ(Ω) are Orlicz spaces. Applying this result, the compactness conditions would be obtained. Hence, we may use Morse theory to obtain existence of nontrivial solutions for problem (N).