arXiv: Classical Analysis and ODEs最新文献_第10页

$C_p$ estimates for rough homogeneous singular integrals and sparse forms 粗糙齐次奇异积分和稀疏形式的C_p估计

arXiv: Classical Analysis and ODEs Pub Date : 2019-09-18 DOI: 10.2422/2036-2145.201910_008

J. Canto, Kangwei Li, L. Roncal, Olli Tapiola

{"title":"$C_p$ estimates for rough homogeneous singular integrals and sparse forms","authors":"J. Canto, Kangwei Li, L. Roncal, Olli Tapiola","doi":"10.2422/2036-2145.201910_008","DOIUrl":"https://doi.org/10.2422/2036-2145.201910_008","url":null,"abstract":"We consider Coifman--Fefferman inequalities for rough homogeneous singular integrals $T_Omega$ and $C_p$ weights. It was recently shown by Li-Perez-Rivera-Rios-Roncal that $$ \u0000|T_Omega |_{L^p(w)} le C_{p,T,w} |Mf|_{L^p(w)} $$ for every $0 max{1,p}$ without using extrapolation theory. Although the bounds we prove are new even in a qualitative sense, we also give the quantitative bound with respect to the $C_q$ characteristic. Our techniques rely on recent advances in sparse domination theory and we actually prove most of our estimates for sparse forms. \u0000Our second goal is to continue the structural analysis of $C_p$ classes. We consider some weak self-improving properties of $C_p$ weights and weak and dyadic $C_p$ classes. We also revisit and generalize a counterexample by Kahanpaa and Mejlbro who showed that $C_p setminus bigcup_{q > p} C_q neq emptyset$. We combine their construction with techniques of Lerner to define an explicit weight class $widetilde{C}_p$ such that $bigcup_{q > p} C_q subsetneq widetilde{C}_p subsetneq C_p$ and every $w in widetilde{C}_p$ satisfies Muckenhoupt's conjecture. In particular, we give a different, self-contained proof for the fact that the $C_{p+varepsilon}$ condition is not necessary for the Coifman--Fefferman inequality and our ideas allow us to consider also dimensions higher than $1$.","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80412492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

Hardy's operator minus identity and power weights 哈迪算子减去恒等和权值

arXiv: Classical Analysis and ODEs Pub Date : 2019-09-10 DOI: 10.1016/j.jfa.2020.108532

M. Strzelecki

引用次数: 13

Weak differentiability for fractional maximal functions of general L functions on domains 定义域上一般L函数的分数阶极大函数的弱可微性

arXiv: Classical Analysis and ODEs Pub Date : 2019-09-10 DOI: 10.1016/j.aim.2020.107144

João P. G. Ramos, Olli Saari, Julian Weigt

引用次数: 8

HARMONIC GRADIENTS ON HIGHER-DIMENSIONAL SIERPIŃSKI GASKETS 高维sierpiŃski垫片上的谐波梯度

arXiv: Classical Analysis and ODEs Pub Date : 2019-08-28 DOI: 10.1142/s0218348x2050108x

L. Brown, Giovanni Ferrer, Gamal Mograby, Luke G. Rogers, K. Sangam

引用次数: 0

On the Nonlinear Impulsive Volterra-Fredholm Integrodifferential Equations. 非线性脉冲Volterra-Fredholm积分微分方程。

arXiv: Classical Analysis and ODEs Pub Date : 2019-08-26 DOI: 10.22075/IJNAA.2020.20005.2117

Pallavi U. Shikhare, Kishor D. Kucche, J. Sousa

引用次数: 0

On a sampling expansion with partial derivatives for functions of several variables 多变量函数的偏导数抽样展开式

arXiv: Classical Analysis and ODEs Pub Date : 2019-08-16 DOI: 10.2298/FIL2010339N

S. Norvidas

引用次数: 0

Two-weight estimates for sparse square functions and the separated bump conjecture 稀疏平方函数的二权估计和分离凹凸猜想

arXiv: Classical Analysis and ODEs Pub Date : 2019-08-07 DOI: 10.1090/tran/8524

S. Kakaroumpas

引用次数: 0

Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates 单侧弦弧域上椭圆算子的微扰。第二部分:非对称算子和Carleson测度估计

arXiv: Classical Analysis and ODEs Pub Date : 2019-08-06 DOI: 10.1090/tran/8148

J. Cavero, S. Hofmann, J. M. Martell, T. Toro

{"title":"Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates","authors":"J. Cavero, S. Hofmann, J. M. Martell, T. Toro","doi":"10.1090/tran/8148","DOIUrl":"https://doi.org/10.1090/tran/8148","url":null,"abstract":"We generalize to the setting of 1-sided chord-arc domains, that is, to domains satisfying the interior Corkscrew and Harnack Chain conditions (these are respectively scale-invariant/quantitative versions of the openness and path-connectedness) and which have an Ahlfors regular boundary, a result of Kenig-Kirchheim-Pipher-Toro, in which Carleson measure estimates for bounded solutions of the equation $Lu=-{rm div}(Anabla u) = 0$ with $A$ being a real (not necessarily symmetric) uniformly elliptic matrix, imply that the corresponding elliptic measure belongs to the Muckenhoupt $A_infty$ class with respect to surface measure on the boundary. We present two applications of this result. In the first one we extend a perturbation result recently proved by Cavero-Hofmann-Martell presenting a simpler proof and allowing non-symmetric coefficients. Second, we prove that if an operator $L$ as above has locally Lipschitz coefficients satisfying certain Carleson measure condition then $omega_Lin A_infty$ if and only if $omega_{L^top}in A_infty$. As a consequence, we can remove one of the main assumptions in the non-symmetric case of a result of Hofmann-Martell-Toro and show that if the coefficients satisfy a slightly stronger Carleson measure condition the membership of the elliptic measure associated with $L$ to the class $A_infty$ yields that the domain is indeed a chord-arc domain.","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81016140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 18

A Wasserstein Inequality and Minimal Green Energy on Compact Manifolds 紧流形上的一个Wasserstein不等式和最小绿色能量

arXiv: Classical Analysis and ODEs Pub Date : 2019-07-21 DOI: 10.1016/J.JFA.2021.109076

S. Steinerberger

引用次数: 18

Averages along the Square Integers: $ell^p$ improving and Sparse Inequalities 沿平方整数的平均值:$ well ^p$改进和稀疏不等式

arXiv: Classical Analysis and ODEs Pub Date : 2019-07-12 DOI: 10.2140/tunis.2021.3.517

R. Han, M. Lacey, Fan Yang

引用次数: 8