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Weighted inequalities and the shape of approach regions

José García, Javier Soria (1999)

Studia Mathematica

We characterize geometric properties of a family of approach regions by means of analytic properties of the class of weights related to the boundedness of the maximal operator associated with this family.

Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces

Sergio Antonio Tozoni (2004)

Studia Mathematica

Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis ( e j ) j ≥ 1 . Given an operator T from L c ∞ ( X ) to L¹(X), we consider the vector-valued extension T̃ of T given by T ̃ ( ∑ j f j e j ) = ∑ j T ( f j ) e j . We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient...

Weyl calculus for complex and real symmetric domains

Jonathan Arazy, Harald Upmeier (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We define the Weyl functional calculus for real and complex symmetric domains, and compute the associated Weyl transform in the rank 1 case.

When is a Riesz distribution a complex measure?

Alan D. Sokal (2011)

Bulletin de la Société Mathématique de France

Let ℛ α be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by α ∈ ℂ . I give an elementary proof of the necessary and sufficient condition for ℛ α to be a locally finite complex measure (= complex Radon measure).

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