Mixed-norm estimates for paraproducts

Cristina Benea, Camil Muscalu

Type: Article

Publication Date: 2017-01-31

Citations: 0

DOI: https://doi.org/10.5802/jedp.643

Abstract

We present a new approach to the study of singular multi-parameter multilinear Fourier multipliers via multiple vector-valued inequalities. This summarizes some of our results from [1] and [2]. The main example is the bi-parameter paraproduct Π⊗Π, for which we prove estimates within the whole range of admissible Lebesgue estimates.

Locations

Journées Équations aux dérivées partielles - View - PDF
French digital mathematics library (Numdam) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Multi-linear operators given by singular multipliers	1999	Camil Muscalu Terence Tao Christoph Thiele
+ PDF Chat	Vector-valued inequalities for families of bilinear Hilbert transforms and applications to bi-parameter problems	2014	Prabath Silva
+ PDF Chat	Uniform estimates for paraproducts and related multilinear multipliers.	2009	Frédéric Bernicot
+	Multi-linear operators given by singular multipliers	2001	Camil Muscalu Terence Tao Christoph Thiele
+ PDF Chat	Multilinear Multiplier Theorems and Applications	2018	Loukas Grafakos Danqing He Hanh Van Nguyen Lixin Yan
+ PDF Chat	Multilinear paraproducts revisited	2015	Loukas Grafakos Danqing He N. J. Kalton Mieczysław Mastyło
+ PDF Chat	Uniform estimates for paraproducts and related multilinear multipliers	2009	Frédéric Bernicot
+ PDF Chat	Variational estimates for paraproducts	2012	Yen Do Camil Muscalu Christoph Thiele
+ PDF Chat	Multilinear paraproducts on Sobolev spaces	2024	Francesco Di Plinio A. Walton Green Brett D. Wick
+	Multilinear paraproducts on Sobolev spaces	2024	Francesco Di Plinio A. Walton Green Brett D. Wick
+	Banach-valued multilinear singular integrals	2015	Francesco Di Plinio Yumeng Ou
+	Mixed-norm estimates for paraproducts	2016	Cristina Benea Camil Muscalu
+	Paraproducts in One and Several Parameters	2005	Michael T. Lacey Jason Metcalfe
+	Paraproducts in One and Several Parameters	2005	Michael T. Lacey Jason Metcalfe
+	Sharp Lower bound estimates for vector-valued and matrix-valued multipliers in $L^p$	2011	Nicholas Boros Alexander Volberg
+	Boundedness of some multi-parameter fiber-wise multiplier operators	2020	Frédéric Bernicot Polona Durcik
+	Mixed estimates for degenerate multi-linear operators associated to simplexes	2014	Robert Kesler
+	Multi-parameter flag Leibniz rules of arbitrary complexity in mixed-norm spaces	2021	Cristina Benea Yujia Zhai
+	Variational estimates for paraproducts	2010	Yen Do Camil Muscalu Christoph Thiele
+ PDF Chat	Multilinear dyadic operators and their commutators	2016	Ishwari Kunwar

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (15)

Action	Title	Year	Authors
+	On Calderon's Conjecture	1999	Michael T. Lacey Christoph Thiele
+ PDF Chat	Multi-parameter paraproducts	2006	Camil Muscalu Jill Pipher Terence Tao Christoph Thiele
+ PDF Chat	On convergence and growth of partial sums of Fourier series	1966	Lennart Carleson
+ PDF Chat	Bi-parameter paraproducts	2004	Camil Muscalu Jill Pipher Terence Tao Christoph Thiele
+	Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle	1993	Carlos E. Kenig Gustavo Ponce Luis Vega
+ PDF Chat	Calderón-Zygmund Operators on Product Spaces	1985	Jean-Lin Journé
+	Multi-parameter hardy spaces via discrete Littlewood-Paley theory	2010	Zhuoping Ruan
+ PDF Chat	Vector-valued inequalities for families of bilinear Hilbert transforms and applications to bi-parameter problems	2014	Prabath Silva
+ PDF Chat	Multiple vector-valued inequalities via the helicoidal method	2016	Cristina Benea Camil Muscalu
+	Pointwise Convergence of Fourier Series	1973	Charles Fefferman