Weighted Poincaré and Sobolev inequalities and estimates for weighted Peano maximal functions. (English) Zbl 0575.42026

Chanillo, Sagun; Wheeden, Richard L.

Am. J. Math. 107, 1191-1226 (1985).

The authors obtain local Poincaré and Sobolev inequalities involving two weight functions. Also weighted Peano derivatives are considered; the Peano derivative formed with a given weight function is estimated in terms of a maximal function involving a second weight function.

Reviewer: R.D.Carmichael

MSC:

42B25

Maximal functions, Littlewood-Paley theory

Keywords:

Poincaré inequality; Sobolev inequality; weight functions; Peano derivative; maximal function