Duality for A∞ weights on the real line

被引：2
作者：
D'Onofrio, Luigi [1 ]
Popoli, Arturo [2 ]
Schiattarella, Roberta [2 ]
机构：
[1] Univ Napoli Parthenope, Dipartimento Studi Econ & Giurid, Via Gen Parisi 13, I-80100 Naples, Italy
[2] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Via Cintia, I-80126 Naples, Italy
来源：
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2016年 / 27卷 / 03期
关键词：
Muckenhoupt weights; Gehring classes; REVERSE HOLDER INEQUALITY; NORM INEQUALITIES; MUCKENHOUPT; INTEGRABILITY;
D O I：
10.4171/RLM/735
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Under the same bounds on G(q)-constants and A(p)-constants, the optimal exponents for sharp inclusions between Gehring G(q)-class of weights and Muckenhoupt A(p)-class (1 < p, q < infinity) are Holder conjugate, if p and q are conjugate. This is a consequence of a representation theorem of A(infinity) weights in terms of W-1,W-r-biSobolev maps and a duality result between G(q) and A(p) classes in dimension one. We prove also that sharp a priori bounds on constants correspond under the Holder conjugate mapping f(t) = t/t-1.
引用
收藏
页码：287 / 308
页数：22
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