Weighted weak type inequalities with variable exponents for Hardy and maximal operators. (English) Zbl 1135.42319

Summary: We characterize the weighted weak type inequalities with variable exponents for the modified Hardy operators and the Hardy-Littlewood maximal operators.


42B25 Maximal functions, Littlewood-Paley theory
26D10 Inequalities involving derivatives and differential and integral operators
Full Text: DOI Euclid


[1] K. F. Andersen and B. Muckenhoupt, Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions, Studia Math. 72 (1982), 9-26. · Zbl 0501.47011
[2] D. Cruz-Uribe, A. Fiorenza and C. J. Neugebauer, The maximal function on variable \(L^p\) spaces, Ann. Acad. Sci. Fenn. Math. 28 (2003), 223-238. · Zbl 1037.42023
[3] L. Dienig, Maximal functions on generalized \(L^{p(x)}\) spaces, Math. Inequal. Appl. 7 (2004), 245-253.
[4] D. E. Edmunds, V. Kokilashvili and A. Meskhi, On the boundedness and compactness of weighted Hardy operators in spaces \(L^{p(x)}\), Georgian Math. J. 12 (1) (2005), 27-44. · Zbl 1099.47030
[5] E. V. Ferreyra, Weighted Lorentz norm inequalities for integral operators, Studia Math. 96 (1990), 125-134. · Zbl 0738.47022
[6] A. Garsia, Topics in almost everywhere convergence , Markham Publishing Co., Chicago. Ill., 1970. · Zbl 0198.38401
[7] V. Kokilashvili and M. Krbec, Weighted inequalities in Lorentz and Orlicz spaces , World Sci. Publishing, River Edge, NJ, 1991. · Zbl 0751.46021
[8] O. Kovavcik and J. Rakosnik, On spaces \(L^{p(x)}\) and \(W^{k,p(x)}\), Czechoslovak Math. J. 41 (116) (1991), no. 4, 592-618.
[9] F. J. Martín-Reyes, New proofs of weighted inequalities for one-sided Hardy-Littlewood maximal functions, Proc. Amer. Math. Soc. 117 (3) (1993), 691-698. · Zbl 0771.42011 · doi:10.2307/2159130
[10] F. J. Martín-Reyes, P. Ortega Salvador and A. de la Torre, Weighted inequalities for one-sided maximal functions, Trans. Amer. Math. Soc. 319 (2) (1990), 517-534. · Zbl 0696.42013 · doi:10.2307/2001252
[11] F. J. Martín-Reyes, P. Ortega and M. D. Sarrión, Boundedness of operators of Hardy type in \(\Lambda^{p,q}\)-spaces and weighted mixed inequalities for singular integral operators, Proc. Royal Soc. Edinburgh 127A (1997), 157-170. · Zbl 0870.46022 · doi:10.1017/S0308210500023556
[12] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. · Zbl 0236.26016 · doi:10.2307/1995882
[13] A. Nekvinda, Hardy-Littlewood maximal operator on \(L^{p(x)}({\mathbf R}^n)\), Math. Inequal. Appl. 7 (2004), 255-265. · Zbl 1059.42016
[14] E. T. Sawyer, Weighted inequalities for the one-sided Hardy-Littlewood maximal functions, Trans. Amer. Math. Soc. 297 (1986), 53-61. · Zbl 0627.42009 · doi:10.2307/2000455
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