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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).

Hessian determinants as elements of dual Sobolev spaces

Teresa Radice (2014)

Studia Mathematica

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.

High order representation formulas and embedding theorems on stratified groups and generalizations

Guozhen Lu, Richard Wheeden (2000)

Studia Mathematica

We derive various integral representation formulas for a function minus a polynomial in terms of vector field gradients of the function of appropriately high order. Our results hold in the general setting of metric spaces, including those associated with Carnot-Carathéodory vector fields, under the assumption that a suitable L 1 to L 1 Poincaré inequality holds. Of particular interest are the representation formulas in Euclidean space and stratified groups, where polynomials exist and L 1 to L 1 Poincaré...

Hilbert spaces of analytic functions of infinitely many variables

O. V. Lopushansky, A. V. Zagorodnyuk (2003)

Annales Polonici Mathematici

We study spaces of analytic functions generated by homogeneous polynomials from the dual space to the symmetric Hilbertian tensor product of a Hilbert space. In particular, we introduce an analogue of the classical Hardy space H² on the Hilbert unit ball and investigate spectral decomposition of unitary operators on this space. Also we prove a Wiener-type theorem for an algebra of analytic functions on the Hilbert unit ball.

Hilbert-valued forms and barriers on weakly pseudoconvex domains.

Vincent Thilliez (1998)

Publicacions Matemàtiques

We introduce an alternative proof of the existence of certain Ck barrier maps, with polynomial explosion of the derivatives, on weakly pseudoconvex domains in Cn. Barriers of this sort have been constructed very recently by J. Michel and M.-C. Shaw, and have various applications. In our paper, the adaptation of Hörmander's L2 techniques to suitable vector-valued functions allows us to give a very simple approach of the problem and to improve some aspects of the result of Michel and Shaw, regarding...

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.

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