Variable Exponent Lebesgue Spaces on Metric Spaces: The Hardy-Littlewood Maximal Operator

By Petteri Harjulehto, P. Hasto, M. Pere. 2005

118 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/fff12a2d292202f45e6486bdae3ee695630f2f70

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In Applied Mathematics

Citations in the corpus

Sobolev embeddings for variable exponent riesz potentials on metric spaces (2006, methodology): “Our first task is then to establish the boundedness of Hardy-Littlewood maximal functions from L p(·) to some Orlicz classes, as an extension of Harjulehto-Hästö- Pere [13] in the case a 1 = 0 on metric setting and the authors' [11, Theorem 2.4] in Euclidean setting.”
Sobolev embeddings in metric measure spaces with variable dimension (2006, background): “Some basic properties of variable exponent Lebesgue spaces on metric measure spaces are given in [19].”
Maximal Operator in Variable Exponent Lebesgue Spaces on Unbounded Quasimetric Measure Spaces (2015, unknown): “These results were quickly generalized from R to the (quasi)metric measure space setting [11], [13], [14].”
Hardy's Inequality in a Variable Exponent Sobolev Space (2005, background): “After Diening’s breakthrough in the study of the Hardy-Littlewood maximal operator [1], there has been great progress in studying various potential-type operators, for the most recent advances see [2, 3, 4, 9, 12, 13].”
Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure (2010, background): “It is known (see [10] for metric measure spaces and [29] for quasimetric measure spaces) that if diam(X)51 and satisfies condition (2), then the condition p2LH(X) implies p2P(1).”
Operators of harmonic analysis in weighted spaces with non-standard growth (2008, background): “Pere [25] and Sobolev embedding theorem with variable exponents on homogeneous spaces with variable dimension was proved in P.”
MAXIMAL FUNCTIONS IN VARIABLE EXPONENT SPACES: LIMITING CASES OF THE EXPONENT (2009, methodology): “[24] P. Harjulehto, P. Hästö and M. Pere: Variable exponent Lebesgue spaces on metric spaces: the Hardy-Littlewood maximal operator, Real Anal.”
Boundedness of Maximal and Singular Operators in Morrey Spaces with Variable Exponent (2008, background): “The following statement is well-known (see [9] for Euclidean spaces and [16] for metric measure spaces).”
Martingale Hardy spaces with variable exponents (2014, background): “An example in [24] showed that log-Hölder continuity of p(x) is essentially the optimal condition when the maximal operator is bounded on variable exponent Lebesgue spaces defined on Euclidean spaces (even in the doubling metric measure spaces; see[14]).”