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Superposition of imbeddings and Fefferman's inequality

Miroslav KrbecThomas Schott — 1999

Bollettino dell'Unione Matematica Italiana

In questo lavoro si studiano condizioni sufficienti sulla funzione peso V , espresse in termini di integrabilità, per la validità della disuguaglianza B u 2 x V x d x 1 2 c B u x 2 d x 1 2 , dove B denota una sfera in R N . Usando una tecnica di decomposizione di immersioni si dimostrano condizioni sufficienti in termini di appartenenza a spazi di Lebesgue, Lorentz-Orlicz e/o di tipo debole. Come applicazioni vengono fornite condizioni sufficienti per la proprietà forte di prolungamento unico per Δ u V u nelle dimensioni 2 e 3.

Indices of Orlicz spaces and some applications

Alberto FiorenzaMiroslav 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.

Critical imbeddings with multivariate rearrangements

Miroslav KrbecHans-Jürgen Schmeisser — 2007

Studia Mathematica

We are concerned with imbeddings of general spaces of Besov and Lizorkin-Triebel type with dominating mixed derivatives in the first critical case. We employ multivariate exponential Orlicz and Lorentz-Orlicz spaces as targets. We study basic properties of the target spaces, in particular, we compare them with usual exponential spaces, showing that in this case the multivariate clones are in fact better adapted to the character of smoothness of the imbedded spaces. Then we prove sharp limiting imbedding...

Decomposition and Moser's lemma.

David E. EdmundsMiroslav Krbec — 2002

Revista Matemática Complutense

Using the idea of the optimal decomposition developed in recent papers (Edmunds-Krbec, 2000) and in Cruz-Uribe-Krbec we study the boundedness of the operator Tg(x) = ∫ g(u)du / u, x ∈ (0,1), and its logarithmic variant between Lorentz spaces and exponential Orlicz and Lorentz-Orlicz spaces. These operators are naturally linked with Moser's lemma, O'Neil's convolution inequality, and estimates for functions with prescribed rearrangement. We give sufficient conditions for and very...

Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm

Paweł ForalewskiHenryk HudzikRadosław KaczmarekMiroslav Krbec — 2013

Commentationes Mathematicae

We first prove that the property of strict monotonicity of a Köthe space ( E , . E ) and/or of its Köthe dual ( E ' , . E ' ) can be used successfully to compare the supports of x E { θ } and y S ( E ' ) , where = x E . Next we prove that any element x S + ( E ) with μ ( T supp x ) = 0 is a point of order smoothness in E , whenever E is an order continuous Köthe space. Finally, we present formulas for the characteristic of monotonicity of Orlicz function spaces endowed with the Orlicz norm in the case when the generating Orlicz function does not satisfy suitable Δ 2 -condition...

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