LEADER 05242nam 22006013 450 001 9910915687303321 005 20231110220026.0 010 $a1-4704-7321-6 035 $a(MiAaPQ)EBC30330566 035 $a(Au-PeEL)EBL30330566 035 $a(CKB)25994213600041 035 $a(EXLCZ)9925994213600041 100 $a20230113d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMulti-Parameter Hardy Spaces Theory and Endpoint Estimates for Multi-Parameter Singular Integrals 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2023. 210 4$dİ2023. 215 $a1 online resource (100 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.281 311 08$aPrint version: Lu, Guozhen Multi-Parameter Hardy Spaces Theory and Endpoint Estimates for Multi-Parameter Singular Integrals Providence : American Mathematical Society,c2023 9781470455378 327 $aCover -- Title page -- Chapter 1. Introduction -- Acknowledgments -- Chapter 2. Single-parameter theory -- 2.1. Singular integral operators and elementary operators -- 2.2. Discrete Littlewood-Paley-Stein theory and Hardy spaces -- 2.3. Endpoint estimate for one-parameter singular integrals -- Chapter 3. Multi-parameter setting: Product theory -- 3.1. Product singular integral operators -- 3.2. Hardy spaces on the product space -- 3.3. Endpoint estimates on product singular integrals -- Chapter 4. General multi-parameter singular integrals and Hardy spaces -- 4.1. Assumptions for vector fields -- 4.2. Multi-parameter Hardy spaces -- 4.3. ^{ } boundedness of multi-parameter singular integrals -- Bibliography -- Back Cover. 330 $a"The main purpose of this paper is to establish the theory of the multi-parameter Hardy spaces Hp (0 [less than] p [less than or equal to] 1) associated to a class of multi-parameter singular integrals extensively studied in the recent book of B. Street (2014), where the Lp (1 [less than] p [less than] [infinity]) estimates are proved for this class of singular integrals. This class of multi-parameter singular integrals are intrinsic to the underlying multi-parameter Carnot-Caratheodory geometry, where the quantitative Frobenius theorem was established by B. Street (2011), and are closely related to both the one-parameter and multi-parameter settings of singular Radon transforms considered by Stein and Street (2011, 2012a, 2012b, 2013). More precisely, Street (2014) studied the Lp (1 [less than] p [less than] [infinity]) boundedness, using elementary operators, of a type of generalized multi-parameter Calderon Zygmund operators on smooth and compact manifolds, which include a certain type of singular Radon transforms. In this work, we are interested in the endpoint estimates for the singular integral operators in both one and multi-parameter settings considered by Street (2014). Actually, using the discrete Littlewood-Paley-Stein analysis, we will introduce the Hardy space Hp (0 [less than] p [less than or equal to] 1) associated with the multi-parameter structures arising from the multi-parameter Carnot-Caratheodory metrics using the appropriate discrete Littlewood-Paley-Stein square functions, and then establish the Hardy space boundedness of singular integrals in both the single and multi-parameter settings. Our approach is much inspired by the work of Street (2014) where he introduced the notions of elementary operators so that the type of singular integrals under consideration can be decomposed into elementary operators"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aHardy spaces 606 $aSingular integrals 606 $aLittlewood-Paley theory 606 $aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Caldero?n-Zygmund, etc.)$2msc 606 $aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory$2msc 606 $aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Hardy-spaces$2msc 615 0$aHardy spaces. 615 0$aSingular integrals. 615 0$aLittlewood-Paley theory. 615 7$aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Caldero?n-Zygmund, etc.). 615 7$aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory. 615 7$aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Hardy-spaces. 676 $a515/.98 676 $a515.98 686 $a42B20$a42B25$a42B30$2msc 700 $aLu$b Guozhen$01778288 701 $aShen$b Jiawei$01778289 701 $aZhang$b Lu$01374884 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910915687303321 996 $aMulti-Parameter Hardy Spaces Theory and Endpoint Estimates for Multi-Parameter Singular Integrals$94301051 997 $aUNINA