Displaying similar documents to “Monge-Ampère measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains”

Extending Hardy fields by non- -germs

Krzysztof Grelowski (2008)

Annales Polonici Mathematici

Similarity:

For a large class of Hardy fields their extensions containing non- -germs are constructed. Hardy fields composed of only non- -germs, apart from constants, are also considered.

Some Banach spaces of Dirichlet series

Maxime Bailleul, Pascal Lefèvre (2015)

Studia Mathematica

Similarity:

The Hardy spaces of Dirichlet series, denoted by p (p ≥ 1), have been studied by Hedenmalm et al. (1997) when p = 2 and by Bayart (2002) in the general case. In this paper we study some L p -generalizations of spaces of Dirichlet series, particularly two families of Bergman spaces, denoted p and p . Each could appear as a “natural” way to generalize the classical case of the unit disk. We recover classical properties of spaces of analytic functions: boundedness of point evaluation, embeddings...

On weighted Hardy spaces on the unit disk

Evgeny A. Poletsky, Khim R. Shrestha (2015)

Banach Center Publications

Similarity:

In this paper we completely characterize those weighted Hardy spaces that are Poletsky-Stessin Hardy spaces H u p . We also provide a reduction of H problems to H u p problems and demonstrate how such a reduction can be used to make shortcuts in the proofs of the interpolation theorem and corona problem.

On contractive projections in Hardy spaces

Florence Lancien, Beata Randrianantoanina, Eric Ricard (2005)

Studia Mathematica

Similarity:

We prove a conjecture of Wojtaszczyk that for 1 ≤ p < ∞, p ≠ 2, H p ( ) does not admit any norm one projections with dimension of the range finite and greater than 1. This implies in particular that for 1 ≤ p < ∞, p ≠ 2, H p does not admit a Schauder basis with constant one.

The maximal theorem for weighted grand Lebesgue spaces

Alberto Fiorenza, Babita Gupta, Pankaj Jain (2008)

Studia Mathematica

Similarity:

We study the Hardy inequality and derive the maximal theorem of Hardy and Littlewood in the context of grand Lebesgue spaces, considered when the underlying measure space is the interval (0,1) ⊂ ℝ, and the maximal function is localized in (0,1). Moreover, we prove that the inequality | | M f | | p ) , w c | | f | | p ) , w holds with some c independent of f iff w belongs to the well known Muckenhoupt class A p , and therefore iff | | M f | | p , w c | | f | | p , w for some c independent of f. Some results of similar type are discussed for the case of small...

The Hausdorff operators on the real Hardy spaces H p ( )

Yuichi Kanjin (2001)

Studia Mathematica

Similarity:

We prove that the Hausdorff operator generated by a function ϕ is bounded on the real Hardy space H p ( ) , 0 < p ≤ 1, if the Fourier transform ϕ̂ of ϕ satisfies certain smoothness conditions. As a special case, we obtain the boundedness of the Cesàro operator of order α on H p ( ) , 2/(2α+1) < p ≤ 1. Our proof is based on the atomic decomposition and molecular characterization of H p ( ) .

Hardy fields in several variables

Leonardo Pasini (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

In questo lavoro si estende il concetto di campo di Hardy [Bou], al contesto dei germi di funzioni in più variabili che sono definite su insiemi semi-algebrici [Br.], [D.] e che risultano essere morfismi di categorie lisce [Pal.]. In tale contesto si dimostra che per ogni campo di Hardy di germi di una fissata categoria liscia 𝒞 , la sua chiusura algebrica relativa nell'anello G 𝒞 , di tutti i germi nella stessa categoria liscia, è un campo di Hardy reale chiuso, che è l'unica chiusura reale...

Hardy fields in several variables

Leonardo Pasini (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

In questo lavoro si estende il concetto di campo di Hardy [Bou], al contesto dei germi di funzioni in più variabili che sono definite su insiemi semi-algebrici [Br.], [D.] e che risultano essere morfismi di categorie lisce [Pal.]. In tale contesto si dimostra che per ogni campo di Hardy di germi di una fissata categoria liscia 𝒞 , la sua chiusura algebrica relativa nell'anello G 𝒞 , di tutti i germi nella stessa categoria liscia, è un campo di Hardy reale chiuso, che è l'unica chiusura reale...

Generalized Hardy spaces on tube domains over cones

Gustavo Garrigos (2001)

Colloquium Mathematicae

Similarity:

We define a class of spaces H μ p , 0 < p < ∞, of holomorphic functions on the tube, with a norm of Hardy type: | | F | | H μ p p = s u p y Ω Ω ̅ | F ( x + i ( y + t ) ) | p d x d μ ( t ) . We allow μ to be any quasi-invariant measure with respect to a group acting simply transitively on the cone. We show the existence of boundary limits for functions in H μ p , and when p ≥ 1, characterize the boundary values as the functions in L μ p satisfying the tangential CR equations. A careful description of the measures μ when their supports lie on the boundary of the cone...

Translations of functions iv vector Hardy classes on the unit disk

Michalak Artur

Similarity:

AbstractThe paper contains studies of relationships between properties of the “translation” mappings T F and the topological and geometric structure of spaces X and Hardy classes h p ( , X ) of X-valued harmonic functions on the open unit disk in ℂ (X is a Banach space). The mapping T F transforming the unit circle of ℂ into h p ( , X ) is associated with a function F h p ( , X ) by the formula T F ( t ) = F ϕ , where ϕₜ is the rotation of through t.AcknowledgmentsThis work is based in part on the author’s doctoral thesis written at...

Maximal operators of Fejér means of double Vilenkin-Fourier series

István Blahota, György Gát, Ushangi Goginava (2007)

Colloquium Mathematicae

Similarity:

The main aim of this paper is to prove that the maximal operator σ * : = s u p | σ n , n | of the Fejér means of the double Vilenkin-Fourier series is not bounded from the Hardy space H 1 / 2 to the space weak- L 1 / 2 .

Commutators of Littlewood-Paley [...] g κ ∗ g κ * -functions on non-homogeneous metric measure spaces

Guanghui Lu, Shuangping Tao (2017)

Open Mathematics

Similarity:

The main purpose of this paper is to prove that the boundedness of the commutator [...] Mκ,b∗ κ , b * generated by the Littlewood-Paley operator [...] Mκ∗ κ * and RBMO (μ) function on non-homogeneous metric measure spaces satisfying the upper doubling and the geometrically doubling conditions. Under the assumption that the kernel of [...] Mκ∗ κ * satisfies a certain Hörmander-type condition, the authors prove that [...] Mκ,b∗ κ , b * is bounded on Lebesgue spaces Lp(μ) for 1 < p < ∞, bounded from...

Hardy-Rogers-type fixed point theorems for α - G F -contractions

Muhammad Arshad, Eskandar Ameer, Aftab Hussain (2015)

Archivum Mathematicum

Similarity:

The aim of this paper is to introduce some new fixed point results of Hardy-Rogers-type for α - η - G F -contraction in a complete metric space. We extend the concept of F -contraction into an α - η - G F -contraction of Hardy-Rogers-type. An example has been constructed to demonstrate the novelty of our results.

Factorization of sequences in discrete Hardy spaces

Santiago Boza (2012)

Studia Mathematica

Similarity:

The purpose of this paper is to obtain a discrete version for the Hardy spaces H p ( ) of the weak factorization results obtained for the real Hardy spaces H p ( ) by Coifman, Rochberg and Weiss for p > n/(n+1), and by Miyachi for p ≤ n/(n+1). It represents an extension, in the one-dimensional case, of the corresponding result by A. Uchiyama who obtained a factorization theorem in the general context of spaces X of homogeneous type, but with some restrictions on the measure that exclude the case...

Multi-dimensional Fejér summability and local Hardy spaces

Ferenc Weisz (2009)

Studia Mathematica

Similarity:

It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space W ( h p , ) to W ( L p , ) . This implies the almost everywhere convergence of the Fejér means in a cone for all f W ( L , ) , which is larger than L ( d ) .

Boundedness of the Hausdorff operators in H p spaces, 0 < p < 1

Elijah Liflyand, Akihiko Miyachi (2009)

Studia Mathematica

Similarity:

Sufficient conditions for the boundedness of the Hausdorff operators in the Hardy spaces H p , 0 < p < 1, on the real line are proved. Two related negative results are also given.

One-sided discrete square function

A. de la Torre, J. L. Torrea (2003)

Studia Mathematica

Similarity:

Let f be a measurable function defined on ℝ. For each n ∈ ℤ we consider the average A f ( x ) = 2 - n x x + 2 f . The square function is defined as S f ( x ) = ( n = - | A f ( x ) - A n - 1 f ( x ) | ² ) 1 / 2 . The local version of this operator, namely the operator S f ( x ) = ( n = - 0 | A f ( x ) - A n - 1 f ( x ) | ² ) 1 / 2 , is of interest in ergodic theory and it has been extensively studied. In particular it has been proved [3] that it is of weak type (1,1), maps L p into itself (p > 1) and L into BMO. We prove that the operator S not only maps L into BMO but it also maps BMO into BMO. We also prove that the L p boundedness...