Interpolation between weighted hardy spaces

Michael Cwikel; John E. Mc Carthy; Thomas H. Wolff

doi:10.1090/S0002-9939-1992-1093595-4

Interpolation between weighted hardy spaces

Michael Cwikel
, John E. Mc Carthy
, Thomas H. Wolff

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We prove that H^p(Ω^1−s₀Ω^s₁) is an interpolation space of exponent s between H^p(Ω₀) and If(Ω₁) if and only if log(Ω₁/Ω₀) is in BMO. If log(Ω₁/Ω₀) fails to be in BMO, H^p(Ω^1−s₀Ω^s₁) can still be an interpolation space, provided the range of Ω has sufficiently large gaps.

Original language	English
Pages (from-to)	381-388
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	116
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1992-1093595-4
State	Published - Oct 1992

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title = "Interpolation between weighted hardy spaces",

abstract = "We prove that Hp(Ω1−s0Ωs1) is an interpolation space of exponent s between Hp(Ω0) and If(Ω1) if and only if log(Ω1/Ω0) is in BMO. If log(Ω1/Ω0) fails to be in BMO, Hp(Ω1−s0Ωs1) can still be an interpolation space, provided the range of Ω has sufficiently large gaps.",

author = "Michael Cwikel and \{Mc Carthy\}, \{John E.\} and Wolff, \{Thomas H.\}",

year = "1992",

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doi = "10.1090/S0002-9939-1992-1093595-4",

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T1 - Interpolation between weighted hardy spaces

AU - Cwikel, Michael

AU - Mc Carthy, John E.

AU - Wolff, Thomas H.

PY - 1992/10

Y1 - 1992/10

N2 - We prove that Hp(Ω1−s0Ωs1) is an interpolation space of exponent s between Hp(Ω0) and If(Ω1) if and only if log(Ω1/Ω0) is in BMO. If log(Ω1/Ω0) fails to be in BMO, Hp(Ω1−s0Ωs1) can still be an interpolation space, provided the range of Ω has sufficiently large gaps.

AB - We prove that Hp(Ω1−s0Ωs1) is an interpolation space of exponent s between Hp(Ω0) and If(Ω1) if and only if log(Ω1/Ω0) is in BMO. If log(Ω1/Ω0) fails to be in BMO, Hp(Ω1−s0Ωs1) can still be an interpolation space, provided the range of Ω has sufficiently large gaps.

UR - https://www.scopus.com/pages/publications/0039297937

U2 - 10.1090/S0002-9939-1992-1093595-4

DO - 10.1090/S0002-9939-1992-1093595-4

M3 - Article

AN - SCOPUS:0039297937

SN - 0002-9939

VL - 116

SP - 381

EP - 388

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -

Interpolation between weighted hardy spaces

Abstract

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