Interpolation of Banach Spaces by the γ-method

Suárez, Jesús; Weis, Lutz

doi:10.1017/cbo9780511721366.015

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Cited by 12 publications

(13 citation statements)

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“…[CJ84,CS88,Voi92]. In [SW06] abstract Stein interpolation was proved for the so-called γ-interpolation method, using the complex formulation of the γ-interpolation method in [KLW21].…”

Section: Introductionmentioning

confidence: 99%

Stein interpolation for the real interpolation method

Lindemulder,

Lorist

2021

Preprint

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“…[CJ84,CS88,Voi92]. In [SW06] abstract Stein interpolation was proved for the so-called γ-interpolation method, using the complex formulation of the γ-interpolation method in [KLW21].…”

Section: Introductionmentioning

confidence: 99%

Stein interpolation for the real interpolation method

Lindemulder,

Lorist

2021

Preprint

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“…Fourier type has been used in many parts of analysis. For instance in interpolation theory [20,53,67], Fourier multiplier theory [9,34,42,62], evolution equations [1,21,63,69], and geometry of Banach spaces [40,41,54,60].…”

Section: Introductionmentioning

confidence: 99%

Extensions of the vector-valued Hausdorff–Young inequalities

Domínguez

Veraar

2021

Math. Z.

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In this paper we study the vector-valued analogues of several inequalities for the Fourier transform. In particular, we consider the inequalities of Hausdorff-Young, Hardy-Littlewood, Paley, Pitt, Bochkarev and Zygmund. The Pitt inequalities include the Hausdorff-Young and Hardy-Littlewood inequalities and state that the Fourier transform is bounded from) under certain condition on p, q, β and γ . Vector-valued analogues are derived under geometric conditions on the underlying Banach space such as Fourier type and related geometric properties. Similar results are derived for T d and Z d by a transference argument. We prove sharpness of our results by providing elementary examples on p -spaces. Moreover, connections with Rademacher (co)type are discussed as well.

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“…[6,8,28]. In [26] Stein interpolation was proved for the so-called -interpolation method, using the complex formulation of the -interpolation method in [17].…”

Section: Introductionmentioning

confidence: 99%

Stein interpolation for the real interpolation method

Lindemulder

Lorist²

2021

Banach J. Math. Anal.

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We prove a complex formulation of the real interpolation method, showing that the real and complex interpolation methods are not inherently real or complex. Using this complex formulation, we prove Stein interpolation for the real interpolation method. We apply this theorem to interpolate weighted $$L^p$$ L p -spaces and the sectoriality of closed operators with the real interpolation method.

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Interpolation of Banach Spaces by the γ-method

Cited by 12 publications

References 0 publications

Stein interpolation for the real interpolation method

Stein interpolation for the real interpolation method

Extensions of the vector-valued Hausdorff–Young inequalities

Stein interpolation for the real interpolation method

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