Some remarks on the Hardy-Littlewood maximal function on variable Lp spaces

By Andrei K. Lerner. 2005

96 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/4baddfa1a64c572027899386e3ae3b54e196264b

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In Applied Mathematics

Citations in the corpus

The fractional maximal operator and fractional integrals on variable $L^p$ spaces (2007, background): “In fact, Lerner [21] has constructed an example to show that p(·) does not need to be continuous.”
MAXIMAL FUNCTIONS IN VARIABLE EXPONENT SPACES: LIMITING CASES OF THE EXPONENT (2009, background): “Lerner [31] constructed examples of variable exponents which are not log-Hölder continuous but for which the maximal operator is nevertheless bounded.”
The Dirichlet Energy Integral and Variable Exponent Sobolev Spaces with Zero Boundary Values (2006, background): “6 guarantee that the Hardy-Littlewood maximal operator is bounded from L( n ) to itself, see [3] and also [4], [21], [23], [18].”
FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, methodology): “We give rearranged proofs of the theorems by Diening [36], Cruz-Uribe, Fiorenza and Neugebauer [26, 27], Nekvinda [161] (2004) and Lerner [102] (2005).”
Musielak–Orlicz–Hardy Spaces Associated with Operators and Their Applications (2012, background): “ [31, 32, 63, 73, 76]) and the motivation to study function spaces of Musielak-Orlicz type is attributed to their extensive applications to many branches of physics and mathematics (see, for example, [11, 12, 13, 14, 31, 32, 63, 64, 68] for more details). In recent years, the study of function space”
New Hardy Spaces of Musielak–Orlicz Type and Boundedness of Sublinear Operators (2011, unknown): “Remark that the class of pointwise multipliers for BMO(Rn) have also recently been used by Lerner [37] for solving a conjecture of Diening (see [17]) on the boundedness of the Hardy–Littlewood maximal operator on the generalized Lebesgue spaces Lp(x)(Rn) (a special case of Musielak–Orlicz spaces, fo”
On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications (2008, unknown): “But for other, weaker results see [9,24,28].”
Bessel potential spaces with variable exponent (2007, background): “For more details see [2], [3], [5], [ 15 ], [17] and [18] where various su‐cient conditions for p(¢) 2 M(Rn) can be found.”
Singular and fractional integral operators on Campanato spaces with variable growth conditions (2010, unknown): “operator, Calderon-Zygmund operators, fractional integral operators (Riesz potentials), etc., see, for example, Diening [3, 4], Diening and Ruiy cka [5], Lerner [ 11 ],”
Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications (2012, background): “Moreover, the motivation to study function spaces of Musielak-Orlicz type is due to that they have wide applications to several branches of physics and mathematics (see, for example, [5, 6, 7, 17, 18, 34, 38, 56] for more details).”
THE BOUNDEDNESS OF CLASSICAL OPERATORS ON VARIABLE L p SPACES (2006, background): “to necessary: see Pick and R˚ uˇziˇcka [35] and [10]. See also the examples in [ 31 ].”
Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates (2013, background): “ (see, for example, [28, 29, 49, 59]) and the motivation to study function spaces of Musielak-Orlicz type is attributed to their extensive applications to many ﬁelds of mathematics (see, for example, [13, 14, 15, 16, 28, 29, 49, 50, 55] for more details). However, it is now understood that there are”
Function spaces of variable smoothness and integrability (2007, background): “However, if one moves beyond assumptions based on continuity moduli, it is possible to derive results also under weaker assumptions, see [14, 39, 43].”