Displaying similar documents to “Growth properties of subharmonic functions in the unit disk”

Complex tangential characterizations of Hardy-Sobolev spaces of holomorphic functions.

Sandrine Grellier (1993)

Revista Matemática Iberoamericana

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Let Ω be a C∞-domain in Cn. It is well known that a holomorphic function on Ω behaves twice as well in complex tangential directions (see [GS] and [Kr] for instance). It follows from well known results (see [H], [RS]) that some converse is true for any kind of regular functions when Ω satisfies (P)    The real tangent space is generated by the Lie brackets of real and imaginary parts of complex tangent vectors ...

Maximal and area integral characterizations of Hardy-Soboley spaces in the unit ball of C.

Patrick Ahern, Joaquim Bruna (1988)

Revista Matemática Iberoamericana

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In this paper we deal with several characterizations of the Hardy-Sobolev spaces in the unit ball of C, that is, spaces of holomorphic functions in the ball whose derivatives up to a certain order belong to the classical Hardy spaces. Some of our characterizations are in terms of maximal functions, area functions or Littlewood-Paley functions involving only complex-tangential derivatives. A special case of our results is a characterization of H itself involving only complex-tangential...

On some spaces of holomorphic functions of exponential growth on a half-plane

Marco M. Peloso, Maura Salvatori (2016)

Concrete Operators

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In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic...