Annales Academię Scientiarum Fennicę

Mathematica

Volumen 33, 2008, 111-119

# NEW BOUNDS FOR *A*_{\infty} WEIGHTS

## Teresa Radice

Universitą 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 ~*G*_{1}(*u*)
and ~*A*_{\infty}(*u*) are studied for weights
*u* : **R**^{n} -> [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*) =
~*G*_{1}(*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 Hölder
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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