Compact bilinear operators and paraproducts revisited

Árpád Bényi; Guopeng Li; Tadahiro Oh; Rodolfo H. Torres

doi:10.4153/S000843952400047X

Compact bilinear operators and paraproducts revisited

Árpád Bényi^*
, Guopeng Li
, Tadahiro Oh
, Rodolfo H. Torres

^*Corresponding author for this work

School of Mathematics and Statistics

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

2 Citations (Scopus)

Abstract

We present a new proof of the compactness of bilinear paraproducts with CMO symbols. By drawing an analogy to compact linear operators, we first explore further properties of compact bilinear operators on Banach spaces and present examples. We then prove compactness of bilinear paraproducts with CMO symbols by combining one of the properties of compact bilinear operators thus obtained with vanishing Carleson measure estimates and interpolation of bilinear compactness.

Original language	English
Pages (from-to)	44-59
Number of pages	16
Journal	Canadian Mathematical Bulletin
Volume	68
Issue number	1
DOIs	https://doi.org/10.4153/S000843952400047X
Publication status	Published - 1 Mar 2025

Keywords

Carleson measure
T(1) theorem
bilinear Calderón-Zygmund operator
compactness
interpolation
paraproduct

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title = "Compact bilinear operators and paraproducts revisited",

abstract = "We present a new proof of the compactness of bilinear paraproducts with CMO symbols. By drawing an analogy to compact linear operators, we first explore further properties of compact bilinear operators on Banach spaces and present examples. We then prove compactness of bilinear paraproducts with CMO symbols by combining one of the properties of compact bilinear operators thus obtained with vanishing Carleson measure estimates and interpolation of bilinear compactness.",

keywords = "Carleson measure, T(1) theorem, bilinear Calder{\'o}n-Zygmund operator, compactness, interpolation, paraproduct",

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T1 - Compact bilinear operators and paraproducts revisited

AU - Bényi, Árpád

AU - Li, Guopeng

AU - Oh, Tadahiro

AU - Torres, Rodolfo H.

N1 - Publisher Copyright: © The Author(s), 2024.

PY - 2025/3/1

Y1 - 2025/3/1

N2 - We present a new proof of the compactness of bilinear paraproducts with CMO symbols. By drawing an analogy to compact linear operators, we first explore further properties of compact bilinear operators on Banach spaces and present examples. We then prove compactness of bilinear paraproducts with CMO symbols by combining one of the properties of compact bilinear operators thus obtained with vanishing Carleson measure estimates and interpolation of bilinear compactness.

AB - We present a new proof of the compactness of bilinear paraproducts with CMO symbols. By drawing an analogy to compact linear operators, we first explore further properties of compact bilinear operators on Banach spaces and present examples. We then prove compactness of bilinear paraproducts with CMO symbols by combining one of the properties of compact bilinear operators thus obtained with vanishing Carleson measure estimates and interpolation of bilinear compactness.

KW - Carleson measure

KW - T(1) theorem

KW - bilinear Calderón-Zygmund operator

KW - compactness

KW - interpolation

KW - paraproduct

UR - https://www.scopus.com/pages/publications/85204654704

U2 - 10.4153/S000843952400047X

DO - 10.4153/S000843952400047X

M3 - Article

AN - SCOPUS:85204654704

SN - 0008-4395

VL - 68

SP - 44

EP - 59

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

IS - 1

ER -

Compact bilinear operators and paraproducts revisited

Abstract

Keywords

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