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Indices of Orlicz spaces and some applications

Alberto Fiorenza, Miroslav Krbec (1997)

Commentationes Mathematicae Universitatis Carolinae

We study connections between the Boyd indices in Orlicz spaces and the growth conditions frequently met in various applications, for instance, in the regularity theory of variational integrals with non-standard growth. We develop a truncation method for computation of the indices and we also give characterizations of them in terms of the growth exponents and of the Jensen means. Applications concern variational integrals and extrapolation of integral operators.

Isomorphisms and several characterizations of Musielak-Orlicz-Hardy spaces associated with some Schrödinger operators

Sibei Yang (2015)

Czechoslovak Mathematical Journal

Let L : = - Δ + V be a Schrödinger operator on n with n 3 and V 0 satisfying Δ - 1 V L ( n ) . Assume that ϕ : n × [ 0 , ) [ 0 , ) is a function such that ϕ ( x , · ) is an Orlicz function, ϕ ( · , t ) 𝔸 ( n ) (the class of uniformly Muckenhoupt weights). Let w be an L -harmonic function on n with 0 < C 1 w C 2 , where C 1 and C 2 are positive constants. In this article, the author proves that the mapping H ϕ , L ( n ) f w f H ϕ ( n ) is an isomorphism from the Musielak-Orlicz-Hardy space associated with L , H ϕ , L ( n ) , to the Musielak-Orlicz-Hardy space H ϕ ( n ) under some assumptions on ϕ . As applications, the author further obtains the...

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