ON SOME NONUNIFORM CASES OF THE WEIGHTED SOBOLEV AND POINCARE INEQUALITIES

被引：10

作者：

Mamedov, F. I. ^{[1
]}

Amanov, R. A. ^{[2
]}

机构：

[1] Azerbaidzhan & Dichle Univ, Natl Acad Sci, Inst Math & Mech, Diyarbakir, Turkey

[2] Natl Acad Sci, Inst Math & Mech, Azerbaidzhan, Turkey

来源：

ST PETERSBURG MATHEMATICAL JOURNAL | 2009年 / 20卷 / 03期

关键词：

Sobolev and Poincare inequalities; Carnot-Caratheodory metric; Besicovitch property; NONLINEAR SUBELLIPTIC EQUATIONS; CARNOT-CARATHEODORY SPACES; VECTOR-FIELDS; REPRESENTATION FORMULAS; DIFFERENTIAL EQUATIONS; HARNACK INEQUALITY; OPERATORS; METRICS; THEOREM;

D O I：

10.1090/S1061-0022-09-01055-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Weighted inequalities parallel to f parallel to(q,nu,B0) <= C Sigma(n)(j=1) parallel to f(xj)parallel to(p,omega j,B0) of Sobolev type (supp f subset of B-0) and of Poincare type ((f) over bar (nu,B0) = 0) are studied, with different weight functions for each partial derivative f(xj), for parallelepipeds B-0 subset of E-n, n >= 1. Also, weighted inequalities parallel to f parallel to(q,nu) <= C parallel to X f parallel to(p,omega) of the same type are considered for vector fields X = {X-j}, j = 1,..., m, with infinitely differentiable coefficients satisfying the Hormander condition.

引用

页码：447 / 463

页数：17

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