Under the same bounds on Gq-constants and Ap-constants, the optimal exponents for sharp inclusions between Gehring Gq-class of weights and Muckenhoupt Ap-class (1 < p; q < ∞) are Holder conjugate, if p and q are conjugate. This is a consequence of a representation theorem of A∞ weights in terms of W1;r-biSobolev maps and a duality result between Gq and Ap classes in dimension one. We prove also that sharp a priori bounds on constants correspond under the Holder conjugate mapping φ(t) = t/t-1.
Measure and integration - Duality for A∞ weights on the real line / D'Onofrio, Luigi., Popoli, A., Schiattarella, Roberta.. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 27:3(2016), pp. 287-308. [10.4171/RLM/735]
Measure and integration - Duality for A∞ weights on the real line
Popoli A.;
2016
Abstract
Under the same bounds on Gq-constants and Ap-constants, the optimal exponents for sharp inclusions between Gehring Gq-class of weights and Muckenhoupt Ap-class (1 < p; q < ∞) are Holder conjugate, if p and q are conjugate. This is a consequence of a representation theorem of A∞ weights in terms of W1;r-biSobolev maps and a duality result between Gq and Ap classes in dimension one. We prove also that sharp a priori bounds on constants correspond under the Holder conjugate mapping φ(t) = t/t-1.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
