Mixed A1-A∞ bounds for fractional integrals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:403

Article

Recchi, Jorgelina

关键词: Maximal operators;    Fractional integrals;    Singular integrals;    Weight norm inequalities;    Sharp bounds;   

DOI  :  10.1016/j.jmaa.2013.02.018

来源: Elsevier

【 摘 要 】

For a fractional integral operator I-alpha we show that parallel to I(alpha)f parallel to(Lq(wq)) <= c[w](A infinity,q)(1/p')[w](A1,q)(1/q) parallel to f parallel to(Lp(wp)) where [w](A infinity.q) equivalent to (Q)sup 1/w(q)(Q) f(Q) M(chi(Q)w(q))dx is Wilson A(infinity.g)'s constant which is smaller than the A(1,q) constant. We also prove a weak type (1, 1) bound for a couple of weights of the form (w, M(alpha)w) assuming that w is an element of A(infinity). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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