WEAK TYPE (1, 1) BEHAVIOR FOR THE LITTLEWOOD–PALEY g-FUNCTION

Xudong Lai

doi:10.4064/cm8854-5-2022

WEAK TYPE (1, 1) BEHAVIOR FOR THE LITTLEWOOD–PALEY g-FUNCTION

Xudong Lai^*

^*Corresponding author for this work

School of Mathematics

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

3 Scopus citations

Abstract

For f ∈ L^p (Rⁿ) (1 ≤ p < ∞), the classical Littlewood–Paley g-function is defined by (^∞) [Formula In Abstract] where u(x, t) denotes the Poisson integral of f. The following two weak type (1, 1) behav-iors for the operator g are established: [Formula In Abstract] for any f ∈ L¹ (Rⁿ), where c_n is the constant in the Poisson kernel and ω_n−1 is the area of the unit sphere in Rⁿ.

Original language	English
Pages (from-to)	285-302
Number of pages	18
Journal	Colloquium Mathematicum
Volume	171
Issue number	2
DOIs	https://doi.org/10.4064/cm8854-5-2022
State	Published - 2023

Keywords

Littlewood–Paley g function
best con-stant
weak type (1, 1) bounds

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title = "WEAK TYPE (1, 1) BEHAVIOR FOR THE LITTLEWOOD–PALEY g-FUNCTION",

abstract = "For f ∈ Lp (Rn) (1 ≤ p < ∞), the classical Littlewood–Paley g-function is defined by (∞) [Formula In Abstract] where u(x, t) denotes the Poisson integral of f. The following two weak type (1, 1) behav-iors for the operator g are established: [Formula In Abstract] for any f ∈ L1 (Rn), where cn is the constant in the Poisson kernel and ωn−1 is the area of the unit sphere in Rn.",

keywords = "Littlewood–Paley g function, best con-stant, weak type (1, 1) bounds",

author = "Xudong Lai",

note = "Publisher Copyright: {\textcopyright} Instytut Matematyczny PAN, 2023.",

year = "2023",

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T1 - WEAK TYPE (1, 1) BEHAVIOR FOR THE LITTLEWOOD–PALEY g-FUNCTION

AU - Lai, Xudong

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PY - 2023

Y1 - 2023

N2 - For f ∈ Lp (Rn) (1 ≤ p < ∞), the classical Littlewood–Paley g-function is defined by (∞) [Formula In Abstract] where u(x, t) denotes the Poisson integral of f. The following two weak type (1, 1) behav-iors for the operator g are established: [Formula In Abstract] for any f ∈ L1 (Rn), where cn is the constant in the Poisson kernel and ωn−1 is the area of the unit sphere in Rn.

AB - For f ∈ Lp (Rn) (1 ≤ p < ∞), the classical Littlewood–Paley g-function is defined by (∞) [Formula In Abstract] where u(x, t) denotes the Poisson integral of f. The following two weak type (1, 1) behav-iors for the operator g are established: [Formula In Abstract] for any f ∈ L1 (Rn), where cn is the constant in the Poisson kernel and ωn−1 is the area of the unit sphere in Rn.

KW - Littlewood–Paley g function

KW - best con-stant

KW - weak type (1, 1) bounds

UR - https://www.scopus.com/pages/publications/85163944062

U2 - 10.4064/cm8854-5-2022

DO - 10.4064/cm8854-5-2022

M3 - 文章

AN - SCOPUS:85163944062

SN - 0010-1354

VL - 171

SP - 285

EP - 302

JO - Colloquium Mathematicum

JF - Colloquium Mathematicum

IS - 2

ER -

WEAK TYPE (1, 1) BEHAVIOR FOR THE LITTLEWOOD–PALEY g-FUNCTION

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Keywords

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