On weak type inequalities for rare maximal functions

• Autorzy: K. Hare , A. Stokolos
• Języki publikacji: EN

Abstrakty

EN

The properties of rare maximal functions (i.e. Hardy-Littlewood maximal functions associated with sparse families of intervals) are investigated. A simple criterion allows one to decide if a given rare maximal function satisfies a converse weak type inequality. The summability properties of rare maximal functions are also considered.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 83
• Numer: 2
• Strony: 173-182

Daty

wydano

2000

otrzymano

1999-05-05

Twórcy

autor

K. Hare

• Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

autor

A. Stokolos

• Department of Mathematics, Odessa State University, Petra Velikogo, 2 270000 Odessa, Ukraine

Bibliografia

• [1] M. de Guzmán, Differentiation of Integrals in $R^n$, Lecture Notes in Math. 481, Springer, 1975.
• [2] G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), 81-116.
• [3] E. M. Stein, Note on the class L logL, Studia Math. 32 (1969), 305-310.
• [4] P. L. Ul'yanov, Embedding of some function classes $H^ω_p$, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 649-686 (in Russian).