Generalized analyticity in UMD spaces

Berkson, Earl; Gillespie, T. A.; Muhly, Paul S.

doi:10.1007/bf02386355

Cited by 40 publications

(40 citation statements)

References 9 publications

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“…The factorization leads to estimates of the form T ≤ c S . It is possible in certain cases to keep S fixed while varying ι, P, thereby improving on c. A classical example is the transference principle by Coifman and Weiss [6,7] in its abstract form given by Berkson et al [2]. It has the form…”

Section: The Transference Resultsmentioning

confidence: 99%

The group reduction for bounded cosine functions on UMD spaces

Haase

2008

Math. Z.

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Section: The Transference Resultsmentioning

confidence: 99%

The group reduction for bounded cosine functions on UMD spaces

Haase

2008

Math. Z.

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“…This fact together with the so-called transference method (see [BGM2]) was used in [DDPS] to establish the following result (which in the special case M=B(H) was first established by E. B. Davies in [Da2] …”

Section: Preliminariesmentioning

confidence: 95%

On Unbounded p-Summable Fredholm Modules

Carey

Phillips

Sukochev

2000

Advances in Mathematics

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“…A general approach to surmounting such difficulties is furnished by Lemma (2.5) of [5], whose proof supplies the following specialized tool for our present situation. (Here and henceforth, given subsets A and B of G, we shall denote by A − B the group -theoretic difference set consisting of all differences a − b such that a ∈ A and b ∈ B.)…”

Section: Transference Of Bisublinear Maximal Estimates From Lca Groupsmentioning

confidence: 99%

Discretization and Transference of Bisublinear Maximal Operators

Berkson

Carro

Gillespie

2006

J Fourier Anal Appl

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Abstract. We develop a general condition for automatically discretizing strong type bisublinear maximal estimates that arise in the context of the real line. In particular, this method applies directly to Michael Lacey's strong type boundedness results for the bisublinear maximal Hilbert transform and for the bisublinear Hardy-Littlewood maximal operator, furnishing the counterpart of each of these two results (without changes to the range of exponents) for the sequence spaces`p (Z). We then take up some transference applications of discretized maximal bisublinear operators to maximal estimates and almost everywhere convergence in Lebesgue spaces of abstract measures. We also broaden the scope of such applications, which are based on transference from Z, by developing general methods for transplanting bisublinear maximal estimates from arbitrary locally compact abelian groups.

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Generalized analyticity in UMD spaces

Cited by 40 publications

References 9 publications

The group reduction for bounded cosine functions on UMD spaces

The group reduction for bounded cosine functions on UMD spaces

On Unbounded p-Summable Fredholm Modules

Discretization and Transference of Bisublinear Maximal Operators

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