THE BOUNDEDNESS OF CLASSICAL OPERATORS ON VARIABLE L p SPACES

By D. Cruz-Uribe, Alberto Fiorenza, J. M. Martell, C. P'erez. 2006

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Citations in the corpus

Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences (2011, unknown): “Indeed, the following lemma is a consequence of [12] and [17, Theorem 4.”
Lorentz spaces with variable exponents (2012, background): “The study of the maximal operator in the frame of Lebesgue spaces with variable exponents attracted a lot of attention with the most important breakthroughs being achieved in [8], [9], [11], [13], [27].”
Global gradient estimates for the $p(\cdot)$-Laplacian (2013, background): “The most advanced form of this result can be found in [9, Theorem 4.3.8]. The boundedness of M has many interesting consequences like Sobolev embeddings and the boundedness of singular integrals, see [4, 9]. In the case of higher-integrability of the p(·)-Laplacian system a slightly stronger conditi”
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].”
Hardy inequality in variable exponent Lebesgue spaces (2007, result): “In the rapidly developing field of ”variable exponent spaces” there have already been made an essential progress in studying classical integral operators, such as maximal and singular operators, Riesz potentials and Hardy operators, we refer for example to the papers [ 3 ], [4], [5], [6], [7], [13],”
Boundedness of Maximal and Singular Operators in Morrey Spaces with Variable Exponent (2008, methodology): “For mapping properties of maximal functions and singular integrals on Lebesgue spaces with variable exponent we refer to [9], [10], [7], [ 6 ], [19]-[20], [26], [13] (see also [29], [17] and references therein).”
Intrinsic Square Function Characterizations of Hardy Spaces with Variable Exponents (2014, unknown): “, [1,2,6,8–13,20,30,43,48,50].”
Weighted Norm Inequalities for Rough Singular Integral Operators (2017, methodology): “ main results from [16, Theorem 2.1], where modular type estimates can be found as well, see [16, Theorem 3.1]. A similar result holds for (unweighted) variable Lp spaces following the main idea from [12]. See Appendix A for some special examples. Ofcourse, Corollary1.2improves inseveral directions ”
The relation between variable Bessel potential spaces and Triebel–Lizorkin spaces (2008, background): “For Lemma 3 , one can see page 251 in 2 and Theorem 4 in ref.”
Weighted Sobolev theorem in Lebesgue spaces with variable exponent (2007, background): “Perez [3], a weaker version being given in V.”