On the growth of vector-valued fourier series

Javier Parcet; Fernando Soria; Quanhua Xu

doi:10.1512/iumj.2013.62.5135

On the growth of vector-valued fourier series

Javier Parcet
, Fernando Soria
, Quanhua Xu

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

4 Scopus citations

Abstract

Let f : T → X satisfy ∫ _T∥f (x) ∥_X(log⁺∥f (x) ∥X)^1+δ dx < ∞, where X is a UMD Banach space and δ > 0. Then, we prove that ∥ ∑_|κ|≤n f̂ ^(κ)e2πiκx∥_x = o(log logn) for almost every x ∈ T. In other words, the "little Carleson theorem" holds for UMDvalued functions.

Original language	English
Pages (from-to)	1765-1784
Number of pages	20
Journal	Indiana University Mathematics Journal
Volume	62
Issue number	6
DOIs	https://doi.org/10.1512/iumj.2013.62.5135
State	Published - 2013
Externally published	Yes

Keywords

Growth of Fourier series
UMD Banach spaces

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title = "On the growth of vector-valued fourier series",

abstract = "Let f : T → X satisfy ∫ T∥f (x) ∥X(log+∥f (x) ∥X)1+δ dx < ∞, where X is a UMD Banach space and δ > 0. Then, we prove that ∥ ∑|κ|≤n {\^f} (κ)e2πiκx∥x = o(log logn) for almost every x ∈ T. In other words, the {"}little Carleson theorem{"} holds for UMDvalued functions.",

keywords = "Growth of Fourier series, UMD Banach spaces",

author = "Javier Parcet and Fernando Soria and Quanhua Xu",

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language = "英语",

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pages = "1765--1784",

journal = "Indiana University Mathematics Journal",

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T1 - On the growth of vector-valued fourier series

AU - Parcet, Javier

AU - Soria, Fernando

AU - Xu, Quanhua

PY - 2013

Y1 - 2013

N2 - Let f : T → X satisfy ∫ T∥f (x) ∥X(log+∥f (x) ∥X)1+δ dx < ∞, where X is a UMD Banach space and δ > 0. Then, we prove that ∥ ∑|κ|≤n f̂ (κ)e2πiκx∥x = o(log logn) for almost every x ∈ T. In other words, the "little Carleson theorem" holds for UMDvalued functions.

AB - Let f : T → X satisfy ∫ T∥f (x) ∥X(log+∥f (x) ∥X)1+δ dx < ∞, where X is a UMD Banach space and δ > 0. Then, we prove that ∥ ∑|κ|≤n f̂ (κ)e2πiκx∥x = o(log logn) for almost every x ∈ T. In other words, the "little Carleson theorem" holds for UMDvalued functions.

KW - Growth of Fourier series

KW - UMD Banach spaces

UR - https://www.scopus.com/pages/publications/84904479711

U2 - 10.1512/iumj.2013.62.5135

DO - 10.1512/iumj.2013.62.5135

M3 - 文章

AN - SCOPUS:84904479711

SN - 0022-2518

VL - 62

SP - 1765

EP - 1784

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 6

ER -

On the growth of vector-valued fourier series

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Keywords

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