Extrapolation and weighted norm inequalities between Lebesgue and Lipschitz spaces in the variable exponent context

GLADIS PRADOLINI; E. ADRIÁN CABRAL; RAMOS WILFREDO ARIEL

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2015

0022-247X

We give extrapolation results starting from weighted inequalities between Lebesgue and Lipschitz spaces,From this hypothesis we obtain a large class of inequalitiesincluding weighted $L^p-L^q$ estimates and weighted $L^p$- Lipschitzintegral spaces, generalizing well know results for certainsublinear operator.From the same hypothesis  we obtain the correspondingresults in the setting of variable exponent spaces. Particularly, weobtain estimates of the type L{p(.)}-variable versions ofLipschitz integral spaces. We also prove a surprising  weightedinequalities of the type L{p(.)}-L{q(.)}.An important tool in order to get the main resultsis an improvement of an estimate due to Calderon and Scott in, which allow us to relate different integral Lipschitz spaces.Our results are new even in the classical context of constant exponents.