Hardy inequalities in function spaces

Hardy Inequalities in Function Spaces

Correlation Inequalities in Function Spaces

We give a condition for a Borel measure on R which is sufficient for the validity of an AD-type correlation inequality in the function space In [1] was proved that if φ1, φ2, φ3, φ4 are bounded real non negative measurable functions on the space with measure (Rn,B, μ) which satisfy for all x̄, ȳ ∈ R the following inequality φ1(x̄)φ2(ȳ) ≤ φ3(x̄ ∨ ȳ)φ4(x̄ ∧ ȳ) a.s., (1) then ∫ φ1(x̄)μ(dx̄) ∫ φ2(x̄)μ(dx̄)...

Wavelet Decomposition Techniques and Hardy Inequalities for Function Spaces on Cellular Domains

A rather tricky question is the construction of wavelet bases on domains for suitable function spaces (Sobolev, Besov, Triebel-Lizorkin type). In his monograph from 2008, Triebel presented an approach how to construct wavelet (Riesz) bases in function spaces of Besov and Triebel-Lizorkin type on cellular domains, in particular on the cube. However, he had to exclude essential exceptional values...

Radial Maximal Function Characterizations for Hardy Spaces on RD-spaces

An RD-space X is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds. The authors prove that for a space of homogeneous type X having “dimension” n, there exists a p0 ∈ (n/(n+ 1), 1) such that for certain classes of distributions, the L(X ) quasi-norms of their radial maximal functions and grand maximal functions are ...

Critical Hardy–Sobolev Inequalities

Abstract We consider Hardy inequalities in IRn, n ≥ 3, with best constant that involve either distance to the boundary or distance to a surface of co-dimension k < n, and we show that they can still be improved by adding a multiple of a whole range of critical norms that at the extreme case become precisely the critical Sobolev norm. Résumé Nous étudions des inegalités de Hardy dans IRn, n ≥ 3,...