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Hardy Inequality in Variable Exponent Lebesgue Spaces

Diening, Lars, Samko, Stefan (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26D10, 46E30, 47B38We prove the Hardy inequality and a similar inequality for the dual Hardy operator for variable exponent Lebesgue spaces.

Harmonic interpolating sequences, L p and BMO

John B. Garnett (1978)

Annales de l'institut Fourier

Let ( z ν ) be a sequence in the upper half plane. If 1 < p ≤ ∞ and if y ν 1 / p f ( z ν ) = a ν , ν = 1 , 2 , ... ( * ) has solution f ( z ) in the class of Poisson integrals of L p functions for any sequence ( a ν ) ∈ ℓ p , then we show that ( z ν ) is an interpolating sequence for H ∞ . If f ( z ν ) = a ν , ν = 1 , 2 , ... has solution in the class of Poisson integrals of BMO functions whenever ( a ν ) ∈ ℓ ∞ , then ( z ν ) is again an interpolating sequence for H ∞ . A somewhat more general theorem is also proved and a counterexample for the case p ≤ 1 is described.

Hausdorff operator on Morrey spaces and Campanato spaces

Jianmiao Ruan, Dashan Fan, Hongliang Li (2020)

Czechoslovak Mathematical Journal

We study the high-dimensional Hausdorff operators on the Morrey space and on the Campanato space. We establish their sharp boundedness on these spaces. Particularly, our results solve an open question posted by E. Liflyand (2013).

Hölder and Lp estimates for the solutions of the ∂-equation in non-smooth strictly pseudoconvex domains.

Josep M. Burgués Badía (1990)

Publicacions Matemàtiques

Let D be a bounded strict pseudoconvex non-smooth domain in Cn. In this paper we prove that the estimates in Lp and Lipschitz classes for the solutions of the ∂-equation with Lp-data in regular strictly pseudoconvex domains (see [2]) are also valid for D. We also give estimates of the same type for the ∂b in the regular part of the boundary of these domains.

Homogenous Banach spaces on the unit circle.

Thomas Vils Pedersen (2000)

Publicacions Matemàtiques

We prove that a homogeneous Banach space B on the unit circle T can be embedded as a closed subspace of a dual space Ξ*B contained in the space of bounded Borel measures on T in such a way that the map B → Ξ*B defines a bijective correspondence between the class of homogeneous Banach spaces on T and the class of prehomogeneous Banach spaces on T.We apply our results to show that the algebra of all continuous functions on T is the only homogeneous Banach algebra on T in which every closed ideal has...

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