Gagliardo–Nirenberg inequalities in regular Orlicz spaces involving nonlinear expressions |
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Authors: | Agnieszka Kaamajska Miroslav Krbec |
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Institution: | aInstitute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland;bInstitute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67 Praha 1, Czech Republic |
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Abstract: | We consider a triple of N-functions (M,H,J) that satisfy the Δ′-condition, and suppose that an additive variant of interpolation inequality holds where , is an arbitrary set invariant with respect to external and internal dilations. We show that the above inequality implies its certain nonlinear variant involving the expressions and . Various generalizations of this inequality to the more general class of N-functions, measures and to higher order derivatives are also discussed and the examples are presented. |
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Keywords: | Gagliardo– Nirenberg inequalities Orlicz spaces |
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