Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves

Oleksiy Karlovych

doi:10.1002/mana.200810295

Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves

Oleksiy Karlovych

DM - Departamento de Matemática

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

8 Citations (Scopus)

Abstract

We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights phi(t,gamma)(tau) = |(tau - t)gamma|, where gamma is a complex number, over arbitrary Carleson Curves. If the curve has different spirality indices at the point t and gamma is not real, then phi(t,gamma) is an oscillating weight lying beyond the class of radial oscillating weights considered recently by V. Kokilashvili, N. Samko, and S. Samko. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim

Original language	Unknown
Pages (from-to)	85-93
Journal	Mathematische Nachrichten
Volume	283
Issue number	1
DOIs	https://doi.org/10.1002/mana.200810295
Publication status	Published - 1 Jan 2010

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10.1002/mana.200810295

Cite this

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title = "Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves",

abstract = "We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights phi(t,gamma)(tau) = |(tau - t)gamma|, where gamma is a complex number, over arbitrary Carleson Curves. If the curve has different spirality indices at the point t and gamma is not real, then phi(t,gamma) is an oscillating weight lying beyond the class of radial oscillating weights considered recently by V. Kokilashvili, N. Samko, and S. Samko. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim",

keywords = "Maximal, submultiplicative, curve, Dini-Lipschitz, weight, operator, Lebesgue, space, Carleson, condition, indices, oscillating, of, function, variable, spirality, l-p(center-dot), weighted",

author = "Oleksiy Karlovych",

year = "2010",

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journal = "Mathematische Nachrichten",

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TY - JOUR

T1 - Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves

AU - Karlovych, Oleksiy

PY - 2010/1/1

Y1 - 2010/1/1

N2 - We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights phi(t,gamma)(tau) = |(tau - t)gamma|, where gamma is a complex number, over arbitrary Carleson Curves. If the curve has different spirality indices at the point t and gamma is not real, then phi(t,gamma) is an oscillating weight lying beyond the class of radial oscillating weights considered recently by V. Kokilashvili, N. Samko, and S. Samko. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim

AB - We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights phi(t,gamma)(tau) = |(tau - t)gamma|, where gamma is a complex number, over arbitrary Carleson Curves. If the curve has different spirality indices at the point t and gamma is not real, then phi(t,gamma) is an oscillating weight lying beyond the class of radial oscillating weights considered recently by V. Kokilashvili, N. Samko, and S. Samko. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim

KW - Maximal

KW - submultiplicative

KW - curve

KW - Dini-Lipschitz

KW - weight

KW - operator

KW - Lebesgue

KW - space

KW - Carleson

KW - condition

KW - indices

KW - oscillating

KW - of

KW - function

KW - variable

KW - spirality

KW - l-p(center-dot)

KW - weighted

U2 - 10.1002/mana.200810295

DO - 10.1002/mana.200810295

M3 - Article

SN - 0025-584X

VL - 283

SP - 85

EP - 93

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 1

ER -