The metric space $H^p(A)$, 0

David M. Boyd

Displaying similar documents to “The metric space $H^{p} (A)$ , 0”

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.

The isoperimetric inequality in the Hardy class $H^{1}$

M. Mateljević (1979)

Matematički Vesnik

Similarity:

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∗ $ℳ_{κ, b}^{*}$ generated by the Littlewood-Paley operator [...] Mκ∗ $ℳ_{κ}^{*}$ 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∗ $ℳ_{κ}^{*}$ satisfies a certain Hörmander-type condition, the authors prove that [...] Mκ,b∗ $ℳ_{κ, b}^{*}$ is bounded on Lebesgue spaces Lp(μ) for 1 < p < ∞, bounded from...

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.

On the tangency of sets in generalized metric spaces for certain functions of the class $F_{ρ}^{*}$

T. Konik (1991)

Matematički Vesnik

Similarity:

The weak type inequality for the Walsh system

Ushangi Goginava (2008)

Studia Mathematica

Similarity:

The main aim of this paper is to prove that the maximal operator $σ^{}$ is bounded from the Hardy space $H_{1 / 2}$ to weak- $L_{1 / 2}$ and is not bounded from $H_{1 / 2}$ to $L_{1 / 2}$ .

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 $H^{\infty}$ 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.

Bounded evaluation operators from $H^{p}$ into $ℓ^{q}$

Martin Smith (2007)

Studia Mathematica

Similarity:

Given 0 < p,q < ∞ and any sequence z = zₙ in the unit disc , we define an operator from functions on to sequences by $T_{z, p} (f) = {(1 - | z ₙ | ²)}^{1 / p} f (z ₙ)$ . Necessary and sufficient conditions on zₙ are given such that $T_{z, p}$ maps the Hardy space $H^{p}$ boundedly into the sequence space $ℓ^{q}$ . A corresponding result for Bergman spaces is also stated.

The Hausdorff operators on the real Hardy spaces $H^{p} (ℝ)$

Yuichi Kanjin (2001)

Studia Mathematica

Similarity:

We prove that the Hausdorff operator generated by a function ϕ is bounded on the real Hardy space $H^{p} (ℝ)$ , 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 $H^{p} (ℝ)$ , 2/(2α+1) < p ≤ 1. Our proof is based on the atomic decomposition and molecular characterization of $H^{p} (ℝ)$ .

Essential norms of weighted composition operators between Hardy spaces $H^{p}$ and $H^{q}$ for 1 ≤ p,q ≤ ∞

R. Demazeux (2011)

Studia Mathematica

Similarity:

We complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces $H^{p}$ and $H^{q}$ for 1 ≤ p,q ≤ ∞. In particular we give some estimates for the cases 1 = p ≤ q ≤ ∞ and 1 ≤ q < p ≤ ∞.

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 $F \in h^{p} (, X)$ by the formula $T_{F} (t) = F \circ ϕ ₜ$ , where ϕₜ is the rotation of through t.AcknowledgmentsThis work is based in part on the author’s doctoral thesis written at...

Continuous rearrangements of the Haar system in $H_{p}$ for 0 < p < ∞

Krzysztof Smela (2008)

Studia Mathematica

Similarity:

We prove three theorems on linear operators $T_{τ, p} : H_{p} (ℬ) \to H_{p}$ induced by rearrangement of a subsequence of a Haar system. We find a sufficient and necessary condition for $T_{τ, p}$ to be continuous for 0 < p < ∞.

Weighted variable $L^{p}$ integral inequalities for the maximal operator on non-increasing functions

C. J. Neugebauer (2009)

Studia Mathematica

Similarity:

Let $B_{p}$ be the Ariõ-Muckenhoupt weight class which controls the weighted $L^{p}$ -norm inequalities for the Hardy operator on non-increasing functions. We replace the constant p by a function p(x) and examine the associated $L^{p (x)}$ -norm inequalities of the Hardy operator.

Adjacent dyadic systems and the $L^{p}$ -boundedness of shift operators in metric spaces revisited

Olli Tapiola (2016)

Colloquium Mathematicae

Similarity:

With the help of recent adjacent dyadic constructions by Hytönen and the author, we give an alternative proof of results of Lechner, Müller and Passenbrunner about the $L^{p}$ -boundedness of shift operators acting on functions $f \in L^{p} (X; E)$ where 1 < p < ∞, X is a metric space and E is a UMD space.

Boundedness of Stein's square functions and Bochner-Riesz means associated to operators on Hardy spaces

Xuefang Yan (2015)

Czechoslovak Mathematical Journal

Similarity:

Let $(X, d, μ)$ be a metric measure space endowed with a distance $d$ and a nonnegative Borel doubling measure $μ$ . Let $L$ be a non-negative self-adjoint operator of order $m$ on $L^{2} (X)$ . Assume that the semigroup $e^{- t L}$ generated by $L$ satisfies the Davies-Gaffney estimate of order $m$ and $L$ satisfies the Plancherel type estimate. Let $H_{L}^{p} (X)$ be the Hardy space associated with $L .$ We show the boundedness of Stein’s square function $𝒢_{δ} (L)$ arising from Bochner-Riesz means associated to $L$ from Hardy spaces $H_{L}^{p} (X)$ to $L^{p} (X)$ , and also study...

Optimal estimates for the fractional Hardy operator

Yoshihiro Mizuta, Aleš Nekvinda, Tetsu Shimomura (2015)

Studia Mathematica

Similarity:

Let $A_{α} f (x) = {| B (0, | x |) |}^{- α / n} \int_{B (0, | x |)} f (t) d t$ be the n-dimensional fractional Hardy operator, where 0 < α ≤ n. It is well-known that $A_{α}$ is bounded from $L^{p}$ to $L^{p_{α}}$ with $p_{α} = n p / (α p - n p + n)$ when n(1-1/p) < α ≤ n. We improve this result within the framework of Banach function spaces, for instance, weighted Lebesgue spaces and Lorentz spaces. We in fact find a ’source’ space $S_{α, Y}$ , which is strictly larger than X, and a ’target’ space $T_{Y}$ , which is strictly smaller than Y, under the assumption that $A_{α}$ is bounded from X into Y and the Hardy-Littlewood...

On linear extension for interpolating sequences

Eric Amar (2008)

Studia Mathematica

Similarity:

Let A be a uniform algebra on X and σ a probability measure on X. We define the Hardy spaces $H^{p} (σ)$ and the $H^{p} (σ)$ interpolating sequences S in the p-spectrum $ℳ_{p}$ of σ. We prove, under some structural hypotheses on A and σ, that if S is a “dual bounded” Carleson sequence, then S is $H^{s} (σ)$ -interpolating with a linear extension operator for s < p, provided that either p = ∞ or p ≤ 2. In the case of the unit ball of ℂⁿ we find, for instance, that if S is dual bounded in $H^{\infty} ()$ then S is $H^{p} ()$ -interpolating with...

A Hardy type inequality for $W_{0}^{m, 1} (Ω)$ functions

Hernán Castro, Juan Dávila, Hui Wang (2013)

Journal of the European Mathematical Society

Similarity:

We consider functions $u \in W_{0}^{m, 1} (Ω)$ , where $Ω \subset ℝ^{N}$ is a smooth bounded domain, and $m \geq 2$ is an integer. For all $j \geq 0, 1 \leq k \leq m - 1$ , such that $1 \leq j + k \leq m$ , we prove that $\frac{\partial^{i} u (x)}{d {(x)}^{m - j - k}} \in W_{0}^{k, 1} (Ω)$ with $∥\partial^{k} {(\frac{\partial^{i} u (x)}{d {(x)}^{m - j - k}})}_{L^{1} (Ω)} \leq C∥ u ∥_{W^{m, 1} (Ω)}$ , where $d$ is a smooth positive function which coincides with dist $(x, \partial Ω)$ near $\partial Ω$ , and $\partial^{l}$ denotes any partial differential operator of order $l$ .

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 $A ₙ f (x) = 2^{- n} \int_{x}^{x + 2 ⁿ} f$ . The square function is defined as $S f (x) = (\sum_{n = - \infty}^{\infty} | A ₙ f (x) - A_{n - 1} f (x) {| ²)}^{1 / 2}$ . The local version of this operator, namely the operator $S ₁ f (x) = (\sum_{n = - \infty}^{0} | A ₙ f (x) - A_{n - 1} f (x) {| ²)}^{1 / 2}$ , 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 $L^{\infty}$ into BMO. We prove that the operator S not only maps $L^{\infty}$ into BMO but it also maps BMO into BMO. We also prove that the $L^{p}$ boundedness...

Radial maximal function characterizations for Hardy spaces on RD-spaces

Loukas Grafakos, Liguang Liu, Dachun Yang (2009)

Bulletin de la Société Mathématique de France

Similarity:

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 $p_{0} \in (n / (n + 1), 1)$ such that for certain classes of distributions, the $L^{p} (𝒳)$ quasi-norms of their radial maximal functions and grand maximal functions are equivalent when $p \in (p_{0}, \infty]$ . This result yields a radial maximal function characterization for Hardy spaces on $𝒳$ . ...

Local integrability of strong and iterated maximal functions

Paul Alton Hagelstein (2001)

Studia Mathematica

Similarity:

Let $M_{S}$ denote the strong maximal operator. Let $M_{x}$ and $M_{y}$ denote the one-dimensional Hardy-Littlewood maximal operators in the horizontal and vertical directions in ℝ². A function h supported on the unit square Q = [0,1]×[0,1] is exhibited such that $\int_{Q} M_{y} M_{x} h < \infty$ but $\int_{Q} M_{x} M_{y} h = \infty$ . It is shown that if f is a function supported on Q such that $\int_{Q} M_{y} M_{x} f < \infty$ but $\int_{Q} M_{x} M_{y} f = \infty$ , then there exists a set A of finite measure in ℝ² such that $\int_{A} M_{S} f = \infty$ .

On the regularity of the one-sided Hardy-Littlewood maximal functions

Feng Liu, Suzhen Mao (2017)

Czechoslovak Mathematical Journal

Similarity:

In this paper we study the regularity properties of the one-dimensional one-sided Hardy-Littlewood maximal operators $ℳ^{+}$ and $ℳ^{-}$ . More precisely, we prove that $ℳ^{+}$ and $ℳ^{-}$ map $W^{1, p} (ℝ) \to W^{1, p} (ℝ)$ with $1 < p < \infty$ , boundedly and continuously. In addition, we show that the discrete versions $M^{+}$ and $M^{-}$ map $BV (ℤ) \to BV (ℤ)$ boundedly and map $l^{1} (ℤ) \to BV (ℤ)$ continuously. Specially, we obtain the sharp variation inequalities of $M^{+}$ and $M^{-}$ , that is, $Var (M^{+} (f)) \leq Var (f) and Var (M^{-} (f)) \leq Var (f)$ if $f \in BV (ℤ)$ , where $Var (f)$ is the total variation of $f$ on $ℤ$ and $BV (ℤ)$ is the set of all functions $f : ℤ \to ℝ$ satisfying $Var (f) < \infty$ .

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 $σ ₀ * : = s u p ₙ | σ_{n, n} |$ of the Fejér means of the double Vilenkin-Fourier series is not bounded from the Hardy space $H_{1 / 2}$ to the space weak- $L_{1 / 2}$ .

On the proximate order of $f^{(s)} (z) * g^{(s)} (z)$ and ${[f (z) * g (z)]}^{(s)}$

M. K. Sen (1971)

Annales Polonici Mathematici

Similarity:

Displaying similar documents to “The metric space H p ( A ) , 0”

Displaying similar documents to “The metric space $H^{p} (A)$ , 0”