# On weak type inequalities for rare maximal functions

Colloquium Mathematicae (2000)

- Volume: 83, Issue: 2, page 173-182
- ISSN: 0010-1354

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topHare, K., and Stokolos, A.. "On weak type inequalities for rare maximal functions." Colloquium Mathematicae 83.2 (2000): 173-182. <http://eudml.org/doc/210779>.

@article{Hare2000,

abstract = {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.},

author = {Hare, K., Stokolos, A.},

journal = {Colloquium Mathematicae},

keywords = {weak type inequalities; rare maximal functions; Hardy-Littlewood maximal functions; summability properties},

language = {eng},

number = {2},

pages = {173-182},

title = {On weak type inequalities for rare maximal functions},

url = {http://eudml.org/doc/210779},

volume = {83},

year = {2000},

}

TY - JOUR

AU - Hare, K.

AU - Stokolos, A.

TI - On weak type inequalities for rare maximal functions

JO - Colloquium Mathematicae

PY - 2000

VL - 83

IS - 2

SP - 173

EP - 182

AB - 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.

LA - eng

KW - weak type inequalities; rare maximal functions; Hardy-Littlewood maximal functions; summability properties

UR - http://eudml.org/doc/210779

ER -

## References

top- [1] M. de Guzmán, Differentiation of Integrals in ${R}^{n}$, Lecture Notes in Math. 481, Springer, 1975. Zbl0327.26010
- [2] G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), 81-116. Zbl56.0264.02
- [3] E. M. Stein, Note on the class L logL, Studia Math. 32 (1969), 305-310. Zbl0182.47803
- [4] P. L. Ul’yanov, Embedding of some function classes ${H}_{p}^{\omega}$, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 649-686 (in Russian).

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