A new characterization of the interpolation spaces between Lp and Lp

Jonathan Arazy; Michael Cwikel

doi:10.7146/math.scand.a-12080

A new characterization of the interpolation spaces between Lp and Lp

Jonathan Arazy
, Michael Cwikel

Department of Mathematics

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

Abstract

It is shown that a normed space X is an interpolation space with respect to the couple (L”, L“) if and only if it is an interpolation space with respect to each of the couples (L', L) and (L”, LTM). The case of spaces with weights is also discussed. Examples are given showing that analogous results do not hold in a more general setting.

Original language	English
Pages (from-to)	253-270
Number of pages	18
Journal	Mathematica Scandinavica
Volume	55
Issue number	2
DOIs	https://doi.org/10.7146/math.scand.a-12080
State	Published - 1984

Access to Document

10.7146/math.scand.a-12080

Cite this

@article{e03480ce34854f0c91dedafdf7881e37,

title = "A new characterization of the interpolation spaces between Lp and Lp",

abstract = "It is shown that a normed space X is an interpolation space with respect to the couple (L{\textquotedblright}, L{\textquotedblleft}) if and only if it is an interpolation space with respect to each of the couples (L', L) and (L{\textquotedblright}, LTM). The case of spaces with weights is also discussed. Examples are given showing that analogous results do not hold in a more general setting.",

author = "Jonathan Arazy and Michael Cwikel",

year = "1984",

doi = "10.7146/math.scand.a-12080",

language = "English",

volume = "55",

pages = "253--270",

journal = "Mathematica Scandinavica",

issn = "0025-5521",

publisher = "Mathematica Scandinavica",

number = "2",

}

TY - JOUR

T1 - A new characterization of the interpolation spaces between Lp and Lp

AU - Arazy, Jonathan

AU - Cwikel, Michael

PY - 1984

Y1 - 1984

N2 - It is shown that a normed space X is an interpolation space with respect to the couple (L”, L“) if and only if it is an interpolation space with respect to each of the couples (L', L) and (L”, LTM). The case of spaces with weights is also discussed. Examples are given showing that analogous results do not hold in a more general setting.

AB - It is shown that a normed space X is an interpolation space with respect to the couple (L”, L“) if and only if it is an interpolation space with respect to each of the couples (L', L) and (L”, LTM). The case of spaces with weights is also discussed. Examples are given showing that analogous results do not hold in a more general setting.

U2 - 10.7146/math.scand.a-12080

DO - 10.7146/math.scand.a-12080

M3 - Article

SN - 0025-5521

VL - 55

SP - 253

EP - 270

JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

IS - 2

ER -

A new characterization of the interpolation spaces between Lp and Lp

Abstract

Access to Document

Fingerprint

Cite this