By Pascal Lefevre, Daniel Li, Herve Queffelec, Luis Rodriguez-piazza

The authors examine composition operators on Hardy-Orlicz areas whilst the Orlicz functionality \Psi grows speedily: compactness, susceptible compactness, to be p-summing, order bounded, \ldots, and convey how those notions behave in response to the expansion of \Psi. They introduce an tailored model of Carleson degree. They build numerous examples exhibiting that their effects are basically sharp. within the final half, they learn the case of Bergman-Orlicz areas

**Read or Download Composition operators on Hardy-Orlicz spaces PDF**

**Best functional analysis books**

Textual content at the concept of services of 1 complicated variable comprises, with many embellishments, the topic of the classes and seminars provided through the writer over a interval of forty years, and may be thought of a resource from which a number of classes will be drawn. as well as the elemental issues within the cl

**Commensurabilities among Lattices in PU (1,n).**

The 1st a part of this monograph is dedicated to a characterization of hypergeometric-like features, that's, twists of hypergeometric features in n-variables. those are handled as an (n+1) dimensional vector house of multivalued in the community holomorphic services outlined at the house of n+3 tuples of exact issues at the projective line P modulo, the diagonal component of car P=m.

This short monograph at the gamma functionality was once designed by means of the writer to fill what he perceived as a spot within the literature of arithmetic, which regularly handled the gamma functionality in a fashion he defined as either sketchy and overly complex. writer Emil Artin, one of many 20th century's prime mathematicians, wrote in his Preface to this booklet, "I suppose that this monograph might help to teach that the gamma functionality should be considered one of many trouble-free services, and that every one of its simple houses will be confirmed utilizing undemanding tools of the calculus.

**Topics in Fourier Analysis and Function Spaces**

Covers a number of sessions of Besov-Hardy-Sobolevtype functionality areas at the Euclidean n-space and at the n-forms, in particular periodic, weighted, anisotropic areas, in addition to areas with dominating mixed-smoothness homes. in line with the newest concepts of Fourier research; the ebook is an up to date, revised, and prolonged model of Fourier research and features areas by means of Hans Triebel.

- Séminaire Pierre Lelong Année 1970-1971
- Grundkurs Funktionalanalysis
- Spectral Theory and Differential Operators
- Theory of Hp Spaces
- Optimal Processes on Manifolds: An Application of Stoke's Theorem

**Additional info for Composition operators on Hardy-Orlicz spaces**

**Example text**

11), with Ψ1 = Ψ2 = Ψ. 3. 16. 1) μ is a Ψ-Carleson measure on D if and only if there exists some constant C ≥ 1 such that : uξ,1−h LΨ (μ) ≤ C Ψ−1 (1/h) , for every ξ ∈ T and every h ∈ (0, 1). 2) μ is a vanishing Ψ-Carleson measure on D if and only if lim sup Ψ−1 (1/h) uξ,1−h h→0 ξ∈T LΨ (μ) = 0. Proof. 12) in the preceding remark. The converse is an obvious consequence of the following lemma. 17. Suppose that there exist A > 0 and h0 ∈ (0, 1) such that: ρμ (h) ≤ 1 , for every h ∈ (0, h0 ). Ψ AΨ−1 (1/h) Then there exists h1 ∈ (0, 1) such that: uξ,1−h LΨ (μ) ≤ 24 , AΨ−1 (1/h) for every ξ ∈ T and every h ∈ (0, h1 ).

24 is not only a technical one, though it might perhaps be weakened. Proof. Let: Ψ(x) = exp (log x)2 e−1/4 x if if √ x ≥ e, √ 0 ≤ x ≤ e. It is plain that Ψ ∈ Δ1 ∩ ∇0 . Moreover, for every A > 0, one has, for h small enough: 1/h = exp − (log A)2 − 2(log A) Ψ AΨ−1 (1/h) log(1/h) . 1.

3 . Once again, the job is done by a discrete measure. (k + 1)! ; yk = ; rk = 1 − 1/3 Ψ(yk ) Ψ(xk ) k x2 < y2 < x3 < · · · . Let ν be the discrete measure deﬁned by: ∞ νk , ν= k=2 where: νk = 1 Ψ (k + 1)! δr k a . k2 so that the series converges. 3 Ψ (k + 1)! that ν is supported in the union of the circles of radii rk and not in a subset of the segment [0, 1] as in the preceding counterexamples. In order to show that (R0 ) is satisﬁed, it is clearly suﬃcient to prove that, when 1 1 ≤h< (with k ≥ 3), we have: Ψ(yk ) Ψ(yk−1 ) Observe that νk ≤ 1 · k1/3 −1 Ψ (1/h) Ψ 2 1 1 , we have Ψ−1 (1/h) ≤ yk so ≤h< Supposing then Ψ(yk ) Ψ(yk−1 ) ρν (h) ≤ k1/3 −1 1 Ψ (1/h) ≤ Ψ (k + 1)!