On -estimates for solutions of elliptic boundary value problems
On anisotropic imbeddings
Proceedings of EQUADIFF 10, Prague, August 27–31, 2001. Preface.
Boundary Value Problems with Bounded Nonlinearity and General Null-Space of the Linear part.
Superposition of imbeddings and Fefferman's inequality
In questo lavoro si studiano condizioni sufficienti sulla funzione peso , espresse in termini di integrabilità, per la validità della disuguaglianza dove denota una sfera in . 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 nelle dimensioni 2 e 3.
Indices of Orlicz spaces and some applications
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
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...
Variations on Yano's extrapolation theorem.
We give very short and transparent proofs of extrapolation theorems of Yano type in the framework of Lorentz spaces. The decomposition technique developed in Edmunds-Krbec (2000) enables us to obtain known and new results in a unified manner.
Decomposition and Moser's lemma.
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...
Dimension-invariant Sobolev imbeddings
We survey recent dimension-invariant imbedding theorems for Sobolev spaces.
Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm
We first prove that the property of strict monotonicity of a Köthe space and/or of its Köthe dual can be used successfully to compare the supports of and , where . Next we prove that any element with is a point of order smoothness in , whenever 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 -condition...
On factorization of Fefferman's inequality
On an optimal decomposition in Zygmund spaces.
A limiting case of the uncertainty principle
Preface
On extrapolation blowups in the scale.
Preface
Moduli and characteristics of monotonicity in some Banach lattices.
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