Strongly nonlinear Gagliardo–Nirenberg inequality in Orlicz spaces and Boyd indices
Claudia Capone
Consiglio Nazionale delle Ricerche, Napoli, ItalyAlberto Fiorenza
Università di Napoli Federico II, Italy and Consiglio Nazionale delle Ricerche, Napoli, ItalyAgnieszka Kałamajska
University of Warsaw, Poland and Polish Academy of Sciences, Warsaw, Poland
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Abstract
Given a N-function and a continuous function satisfying certain assumptions, we derive the inequality
with constants independent of , where belongs locally to the Sobolev space , has compact support, is smaller than the lower Boyd index of , is certain nonlinear transform depending of but not of and denotes the Hardy–Littlewood maximal function. Moreover, we show that when , then can be improved by . This inequality generalizes a previous result by the third author and Peszek, which was dealing with .
Cite this article
Claudia Capone, Alberto Fiorenza, Agnieszka Kałamajska, Strongly nonlinear Gagliardo–Nirenberg inequality in Orlicz spaces and Boyd indices. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 1, pp. 119–141
DOI 10.4171/RLM/755