On modular inequalities in variable L p spaces
作者： Andrei K. Lerner
DOI: 10.1007/S00013-005-1302-5
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摘要: We show that the Hardy-Littlewood maximal operator and a class of Calderon-Zygmund singular integrals satisfy strong type modular inequality in variable L p spaces if only exponent p(x) ∼ const.
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C. J. Neugebauer, D. Cruz-Uribe, A. Firorenza, The maximal function on variable spaces. Annales Academiae Scientiarum Fennicae. Mathematica. ,vol. 28, pp. 223- 238 ,(2003)
José García-Cuerva, J.-L. Rubio de Francia, Weighted norm inequalities and related topics ,(1985)
Julian Musielak, Orlicz Spaces and Modular Spaces ,(1983)
Sergei V. Hruščev, A description of weights satisfying the _{∞} condition of Muckenhoupt Proceedings of the American Mathematical Society. ,vol. 90, pp. 253- 257 ,(1984) , 10.1090/S0002-9939-1984-0727244-4
A. Yu. Karlovich, A. K. Lerner, Commutators of singular integrals on generalized $L^p$ spaces with variable exponent Publicacions Matematiques. ,vol. 49, pp. 111- 125 ,(2005) , 10.5565/PUBLMAT_49105_05
Diego Gallardo, Orlicz spaces for which the Hardy-Littlewood maximal operators is bounded Publicacions Matematiques. ,vol. 32, pp. 261- 266 ,(1988) , 10.5565/37563
L. Diening, M. Ruicka, Calderón-Zygmund operators on generalized Lebesgue spaces $L^{p(\cdot)}$ and problems related to fluid dynamics Crelle's Journal. ,vol. 2003, ,(2003) , 10.1515/CRLL.2003.081
Luboš Pick, Michael Růžička, An example of a space Lp(x) on which the Hardy-Littlewood maximal operator is not bounded Expositiones Mathematicae. ,vol. 19, pp. 369- 371 ,(2001) , 10.1016/S0723-0869(01)80023-2
L. Diening, Maximal function on generalized Lebesgue spaces $L^{p(\cdot)}$ Mathematical Inequalities & Applications. ,vol. 7, pp. 245- 253 ,(2004) , 10.7153/MIA-07-27
Aleš Nekvinda, Hardy-Littlewood maximal operator on L^p(x) (ℝ) Mathematical Inequalities & Applications. pp. 255- 265 ,(2004) , 10.7153/MIA-07-28