The maximal function on variable spaces.

By D. Cruz-Uribe, A. Firorenza, C. Neugebauer. 2003

309 citations recorded by the source corpus.

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Citations in the corpus

On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators (2005, methodology): “Weak type estimate for the maximal operator in the case of variable p was given in the paper by Cruz-Uribe et al. [ 41 , 42].”
Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators (2005, background): “(see, for instance, [ 3 ,26]); namely, we suppose that p∗(x) − p∗(y) A∞ ln 1 |x−y|”
2-Microlocal Besov and Triebel-Lizorkin Spaces of Variable Integrability (2009, methodology): “Inspired by this work, Cruz-Uribe, Fiorenza and Neugebauer in [5] and Nekvinda in [24] removed the p is constant condition by less restrictive conditions.”
Characterization of Riesz and Bessel potentials on variable Lebesgue spaces (2006, methodology): “The general case of the exponent p(¢) non-constant at inflnity, was considered in [18], where some integral condition was imposed and in [ 3 ] where it was assumed that the exponent is log-H˜older continuous at inflnity:”
Operators of harmonic analysis in weighted spaces with non-standard growth (2008, background): “Neugebauer [ 11 ], L. Diening [13–15], L. Diening and M. Ruiy cka [17], V. Kokilashvili, N. Samko and S. Samko [38], V. Kokilashvili and S. Samko [41–43,45], A. Nekvinda [58], S. Samko [70–72], S. Samko, E. Shargorodsky and B. Vakulov [74] and references therein.”
The maximal operator on generalized Orlicz spaces (2015, background): “It was Diening [5] who opened the floodgate by proving the boundedness of the maximal operator under natural and essentially optimal conditions on the exponent (see also [4, 15, 18]).”
VARIABLE BESOV AND TRIEBEL-LIZORKIN SPACES (2008, background): “omit the details here, one can see [ 3 ], [4], [5], [7], [14], [15].”
Sobolev embeddings for variable exponent riesz potentials on metric spaces (2006, background): “For the boundedness of maximal functions in general domains, see Cruz-Uribe, Fiorenza and Neugebauer [ 2 ].”
THE HERZ-TYPE HARDY SPACES WITH VARIABLE EXPONENT AND THEIR APPLICATIONS (2012, background): “There exist some sufficient conditions on p(·) such that the maximal operator M is bounded on Lp(·)(Rn), see [1-4, 11, 12].”
Function spaces of variable smoothness and integrability (2007, methodology): “Building on [ 12 ] and [13] it is shown in [15, Theorem 3.6] that”