Annales AcademiŠ Scientiarum FennicŠ
Mathematica
Volumen 33, 2008, 111-119

NEW BOUNDS FOR A\infty WEIGHTS

Teresa Radice

UniversitÓ degli Studi di Napoli "Federico II", Dipartimento di Matematica e Applicazioni "R. Caccioppoli"
Via Cintia, 80126 Napoli, Italy; teresa.radice 'at' unina.it

Abstract. Two new constants ~G1(u) and ~A\infty(u) are studied for weights u : Rn -> [0,\infty), which are simultaneously finite exactly for A\infty weights. The special case v = h', w = (h-1)' where h : R -> R is an increasing homeomorphism induces the identity ~A\infty(w) = ~G1(v). Other identities are established for such constants, when different measures are involved.

2000 Mathematics Subject Classification: Primary 26D15, 42B25, 46E30.

Key words: Muckenhoupt weights, reverse H÷lder inequalities.

Reference to this article: T. Radice: New bounds for A\infty weights. Ann. Acad. Sci. Fenn. Math. 33 (2008), 111-119.

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