Displaying similar documents to “Atomic decomposition on Hardy-Sobolev spaces”

A Note on Div-Curl Lemma

Gala, Sadek (2007)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 42B30, 46E35, 35B65. We prove two results concerning the div-curl lemma without assuming any sort of exact cancellation, namely the divergence and curl need not be zero, and d i v ( u − v → ) ∈ H 1 ( R d ) which include as a particular case, the result of [3].

Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications

Xiaming Chen, Renjin Jiang, Dachun Yang (2016)

Analysis and Geometry in Metric Spaces

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Let Ω ⊂ Rn be a strongly Lipschitz domain. In this article, the authors study Hardy spaces, Hpr (Ω)and Hpz (Ω), and Hardy-Sobolev spaces, H1,pr (Ω) and H1,pz,0 (Ω) on , for p ∈ ( n/n+1, 1]. The authors establish grand maximal function characterizations of these spaces. As applications, the authors obtain some div-curl lemmas in these settings and, when is a bounded Lipschitz domain, the authors prove that the divergence equation div u = f for f ∈ Hpz (Ω) is solvable in H1,pz,0 (Ω) with...

Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces

Viktor I. Burenkov, Huseyn V. Guliyev (2004)

Studia Mathematica

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The problem of boundedness of the Hardy-Littewood maximal operator in local and global Morrey-type spaces is reduced to the problem of boundedness of the Hardy operator in weighted L p -spaces on the cone of non-negative non-increasing functions. This allows obtaining sufficient conditions for boundedness for all admissible values of the parameters. Moreover, in case of local Morrey-type spaces, for some values of the parameters, these sufficient conditions are also necessary.

Pointwise inequalities of logarithmic type in Hardy-Hölder spaces

Slim Chaabane, Imed Feki (2014)

Czechoslovak Mathematical Journal

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We prove some optimal logarithmic estimates in the Hardy space H ∞ ( G ) with Hölder regularity, where G is the open unit disk or an annular domain of ℂ . These estimates extend the results established by S. Chaabane and I. Feki in the Hardy-Sobolev space H k , ∞ of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality for Hölder functions. As an application of these estimates, we study the stability of both the...

A new characterization of the Sobolev space

Piotr Hajłasz (2003)

Studia Mathematica

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The purpose of this paper is to provide a new characterization of the Sobolev space W 1 , 1 ( ℝ ⁿ ) . We also show a new proof of the characterization of the Sobolev space W 1 , p ( ℝ ⁿ ) , 1 ≤ p < ∞, in terms of Poincaré inequalities.

On limiting embeddings of Besov spaces

V. I. Kolyada, A. K. Lerner (2005)

Studia Mathematica

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We investigate the classical embedding B p , θ s ⊂ B q , θ s - n ( 1 / p - 1 / q ) . The sharp asymptotic behaviour as s → 1 of the operator norm of this embedding is found. In particular, our result yields a refinement of the Bourgain, Brezis and Mironescu theorem concerning an analogous problem for the Sobolev-type embedding. We also give a different, elementary proof of the latter theorem.

Hardy-Sobolev Inequalities for Hessian Integrals

Nunzia Gavitone (2007)

Bollettino dell'Unione Matematica Italiana

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Using appropriate symmetrization arguments, we prove the Hardy-Sobolev type inequalities for Hessian Integrals which extend the classical results, well known for Sobolev functions. For such inequalities the value of the best constant is given. Finally we give an improvement of these inequalities by adding a second term that, involves another singular weight which is a suitable negative power of log ⁡ ( | x | ) .

Growth estimates for generalized factors of H p spaces

Joseph A. Cima, Angeliki Kazas, Michael I. Stessin (2003)

Studia Mathematica

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With φ an inner function and M φ the multiplication operator on a given Hardy space it is known that for any given function f in the Hardy space we may use the Wold decomposition to obtain a factorization of the given f (not the Riesz factorization). This new factorization has been shown to be useful in the study of commutants of Toeplitz operators. We study the smoothness of each factor of this factorization. We show in some cases that the factors lie in the same Hardy space (or smoothness...

Weighted multi-parameter mixed Hardy spaces and their applications

Wei Ding, Yun Xu, Yueping Zhu (2022)

Czechoslovak Mathematical Journal

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Applying discrete Calderón’s identity, we study weighted multi-parameter mixed Hardy space H mix p ( ω , ℝ n 1 × ℝ n 2 ) . Different from classical multi-parameter Hardy space, this space has characteristics of local Hardy space and Hardy space in different directions, respectively. As applications, we discuss the boundedness on H mix p ( ω , ℝ n 1 × ℝ n 2 ) of operators in mixed Journé’s class.

Hessian determinants as elements of dual Sobolev spaces

Teresa Radice (2014)

Studia Mathematica

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In this short note we present new integral formulas for the Hessian determinant. We use them for new definitions of Hessian under minimal regularity assumptions. The Hessian becomes a continuous linear functional on a Sobolev space.

On the Choquet integrals associated to Bessel capacities

Keng Hao Ooi (2022)

Czechoslovak Mathematical Journal

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We characterize the Choquet integrals associated to Bessel capacities in terms of the preduals of the Sobolev multiplier spaces. We make use of the boundedness of local Hardy-Littlewood maximal function on the preduals of the Sobolev multiplier spaces and the minimax theorem as the main tools for the characterizations.

Factorization of sequences in discrete Hardy spaces

Santiago Boza (2012)

Studia Mathematica

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The purpose of this paper is to obtain a discrete version for the Hardy spaces H p ( ℤ ) of the weak factorization results obtained for the real Hardy spaces H p ( ℝ ⁿ ) 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...

On a variant of the Hardy inequality between weighted Orlicz spaces

Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba (2009)

Studia Mathematica

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Let M be an N-function satisfying the Δ₂-condition, and let ω, φ be two other functions, with ω ≥ 0. We study Hardy-type inequalities ∫ ℝ ₊ M ( ω ( x ) | u ( x ) | ) e x p ( - φ ( x ) ) d x ≤ C ∫ ℝ ₊ M ( | u ' ( x ) | ) e x p ( - φ ( x ) ) d x , where u belongs to some set of locally absolutely continuous functions containing C ₀ ∞ ( ℝ ₊ ) . We give sufficient conditions on the triple (ω,φ,M) for such inequalities to be valid for all u from a given set . The set may be smaller than the set of Hardy transforms. Bounds for constants are also given, yielding classical Hardy inequalities with best constants. ...

Holomorphic Sobolev spaces on the ball

Frank Beatrous, Jacob Burbea

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CONTENTSIntroduction ..............................................................50. Preliminaries and notation....................................61. Hilbert spaces of holomorphic functions..............112. Some estimates ..................................................163. The space L q p ............................................224. Norm estimates...................................................305. Sobolev norms....................................................356. Projections...