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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. 119–141DOI 10.4171/RLM/755