WEAK DIFFERENTIABILITY FOR FRACTIONAL MAXIMAL ...Regularity of the Hardy?Littlewood maximal function of a Sobolev function was ... |f(y)| dy, and it defines a bounded operator Lp(Rn) ? Lq(Rn) when q = np/(n ? p) and p > 1. ... Lp spaces with 1 ? p ? n/(n ? 1) where the argument in [12] fails to give any result. ... The weak derivatives are defined using test functions in C?. Lecture Notes on Introduction to Harmonic AnalysisThe distribution function and weak Lp spaces. . . . . . . . . . . 36 ... Hardy-Littlewood maximal function . ... More topics on Sobolev spaces with p = 2 . ... space E which consists of continuous linear functionals on the (widest test function) ... From the proof of Theorem 1.35, we have seen that for any q ? 1, ?k q is. LEBESGUE POINTS IN VARIABLE EXPONENT SPACESto the setting of variable exponent Lebesgue and Sobolev spaces. ... cient for the Hardy?Littlewood maximal operator to be bounded from Lp( · )(Rn) ... By Proposition 4.4 we can use Mu/? = Mu/? as a test ... exists for every x ? Rn E. The function u? is the p( · )-quasicontinuous repre- ... outside the set E for any finite q. Weights arising from parabolicpartialdifferential equations - Aalto MathPublication II: ?Local to global results for spaces of BMO type?. The author has ... such equations is the one associated with the p-Laplace equation ... acterized the good weights for the Hardy-Littlewood maximal function. Mf(x) := sup ... q is sufficient for the Lq(w)-boundedness of the related maximal operator ... Universit`a degli Studi di Napoli ?Federico II? On the Lp ... - fedOAspace Lp. Moreover, in dimension n = 2 we find a number of quantitative sharp ... Stampacchia and Weinberger [LSW], which also proves the following Wiener test to charac- ... (? > 0) and, for any Q ? ?B, the non tangential maximal function, ... denote the Hardy-Littlewood maximal operator associated to ? on ?B (see ... ReferencesSharp Ulyanov and Kolyada inequalities in Hardy spaces. 87. 12. (Lp ... In this paper, we mostly deal with the Lp(Td)-setting. ... mating the moduli of smoothness of a function in Lq in terms of its moduli of smooth- ... Lip(?, p) ?? Lip(? ? ?, q), ... [11] D. Burkholder, R. Gundy, M. Silverstein, A maximal function ... PROBLEMS ON AVERAGES AND LACUNARY MAXIMAL ...Haroske, D.D.: Envelopes and Sharp Embeddings of Function Spaces. ... Mattila, P.: Geometry of Sets and Measures in Euclidean Spaces Fractals and ... Abu-?Shammala, W., Torchinsky, A.: The Hardy-Lorentz spaces Hp,q (Rn). ... F., Frasca?, M., Morrey spaces and Hardy?Littlewood maximal function. ... test functions, 42.
