Endpoint boundedness of toroidal pseudo-differential operators

被引：0

作者：

Ramla, Benhamoud ^{[1
]}

机构：

[1] Zhejiang Normal Univ, Sch Math Sci, Jinhua 321004, Zhejiang, Peoples R China

来源：

OPEN MATHEMATICS | 2024年 / 22卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Torus; toroidal pseudo-differential operator; toroidal Hormander symbol; BMO(T-n); CONTINUITY;

D O I：

10.1515/math-2024-0023

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note, we prove that the toroidal pseudo-differential operator is bounded from L-infinity(T-n)to BMO(Tn) if the symbol belongs to the toroidal Hormander class Sn(rho-1)/2 rho,delta(TnxZn)S rho, with 0<rho <= 1 and 0 <=delta<1 . As a corollary, we obtain a result of toroidal pseudo-differential operators on L-p when 2<p<infinity 2<p<infinity for symbols in the class S(rho,delta)(m)m(T(n)xZ(n)) with m <= n(rho-1)(1/2-1/p)+npmin{0,rho-delta} .

引用

页数：12

共 27 条

[11] PSEUDODIFFERENTIAL OPERATORS WITH NONREGULAR SYMBOLS [J].

CHING, CH .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1972, 11 (02) :436-&

[12]

Delgado J., 2013, Oper. Theory Adv. Appl, V231, P103, DOI [10.1007/978-3-0348-0585-86, DOI 10.1007/978-3-0348-0585-86, 10.1007/978-3-0348-0585-8_6]

[13] LP-BOUNDS FOR PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS [J].

Delgado, Julio ;

Ruzhansky, Michael .

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2019, 18 (03) :531-559

[14] Intrinsic pseudo-differential calculi on any compact Lie group [J].

Fischer, Veronique .

JOURNAL OF FUNCTIONAL ANALYSIS, 2015, 268 (11) :3404-3477

[15] Some Notes on Endpoint Estimates for Pseudo-differential Operators [J].

Guo, Jingwei ;

Zhu, Xiangrong .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (06)

[16] PSEUDO-DIFFERENTIAL OPERATORS [J].

HORMANDE.L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1965, 18 (03) :501-&

[17] L2 CONTINUITY OF PSEUDO-DIFFERENTIAL OPERATORS [J].

HORMANDER, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1971, 24 (04) :529-+

[18] ON THE L-2 CONTINUITY OF PSEUDODIFFERENTIAL-OPERATORS [J].

HOUNIE, J .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1986, 11 (07) :765-778

[19]

Hrmander L., 1967, Pseudo-differential operators and hypoelliptic equations., P138

[20] Ψ-pseudodifferential operators and estimates for maximal oscillatory integrals [J].

Kenig, Carlos E. ;

Staubach, Wolfgang .

STUDIA MATHEMATICA, 2007, 183 (03) :249-258

← 1 2 3 →