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An atomic decomposition of the predual of BMO(ρ).

Beatriz E. Viviani — 1987

Revista Matemática Iberoamericana

We study the Orlicz type spaces H, defined as a generalization of the Hardy spaces H for p ≤ 1. We obtain an atomic decomposition of H, which is used to provide another proof of the known fact that BMO(ρ) is the dual space of H (see S. Janson, 1980, [J]).

Homeomorphisms acting on Besov and Triebel-Lizorkin spaces of local regularity ψ(t).

Silvia I. HartzsteinBeatriz E. Viviani — 2005

Collectanea Mathematica

The aim of this paper is to show that the integral and derivative operators defined by local regularities are homeomorphisms for generalized Besov and Triebel-Lizorkin spaces with local regularities. The underlying geometry is that of homogeneous type spaces and the functions defining local regularities belong to a larger class of growth functions than the potentials t, related to classical fractional integral and derivative operators and Besov and Triebel-Lizorkin spaces.

Integral and derivative operators of functional order on generalized Besov and Triebel-Lizorkin spaces in the setting of spaces of homogeneous type

Silvia I. HartzsteinBeatriz E. Viviani — 2002

Commentationes Mathematicae Universitatis Carolinae

In the setting of spaces of homogeneous-type, we define the Integral, I φ , and Derivative, D φ , operators of order φ , where φ is a function of positive lower type and upper type less than 1 , and show that I φ and D φ are bounded from Lipschitz spaces Λ ξ to Λ ξ φ and Λ ξ / φ respectively, with suitable restrictions on the quasi-increasing function ξ in each case. We also prove that I φ and D φ are bounded from the generalized Besov B ˙ p ψ , q , with 1 p , q < , and Triebel-Lizorkin spaces F ˙ p ψ , q , with 1 < p , q < , of order ψ to those of order φ ψ and ψ / φ respectively,...

On the composition of the integral and derivative operators of functional order

Silvia I. HartzsteinBeatriz E. Viviani — 2003

Commentationes Mathematicae Universitatis Carolinae

The Integral, I φ , and Derivative, D φ , operators of order φ , with φ a function of positive lower type and upper type less than 1 , were defined in [HV2] in the setting of spaces of homogeneous-type. These definitions generalize those of the fractional integral and derivative operators of order α , where φ ( t ) = t α , given in [GSV]. In this work we show that the composition T φ = D φ I φ is a singular integral operator. This result in addition with the results obtained in [HV2] of boundedness of I φ and D φ or the T 1 -theorems proved...

Relations between weighted Orlicz and B M O φ spaces through fractional integrals

Eleonor Ofelia HarboureOscar SalinasBeatriz E. Viviani — 1999

Commentationes Mathematicae Universitatis Carolinae

We characterize the class of weights, invariant under dilations, for which a modified fractional integral operator I α maps weak weighted Orlicz - φ spaces into appropriate weighted versions of the spaces B M O ψ , where ψ ( t ) = t α / n φ - 1 ( 1 / t ) . This generalizes known results about boundedness of I α from weak L p into Lipschitz spaces for p > n / α and from weak L n / α into B M O . It turns out that the class of weights corresponding to I α acting on weak - L φ for φ of lower type equal or greater than n / α , is the same as the one solving the problem for weak...

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