# Weighted weak type inequalities for certain maximal functions

Studia Mathematica (1991)

- Volume: 101, Issue: 1, page 105-111
- ISSN: 0039-3223

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topAimar, Hugo, and Forzani, Liliana. "Weighted weak type inequalities for certain maximal functions." Studia Mathematica 101.1 (1991): 105-111. <http://eudml.org/doc/215889>.

@article{Aimar1991,

abstract = {We give an A\_p type characterization for the pairs of weights (w,v) for which the maximal operator Mf(y) = sup 1/(b-a) ʃ\_a^b |f(x)|dx, where the supremum is taken over all intervals [a,b] such that 0 ≤ a ≤ y ≤ b/ψ(b-a), is of weak type (p,p) with weights (w,v). Here ψ is a nonincreasing function such that ψ(0) = 1 and ψ(∞) = 0.},

author = {Aimar, Hugo, Forzani, Liliana},

journal = {Studia Mathematica},

keywords = {weighted weak type inequalities; maximal functions},

language = {eng},

number = {1},

pages = {105-111},

title = {Weighted weak type inequalities for certain maximal functions},

url = {http://eudml.org/doc/215889},

volume = {101},

year = {1991},

}

TY - JOUR

AU - Aimar, Hugo

AU - Forzani, Liliana

TI - Weighted weak type inequalities for certain maximal functions

JO - Studia Mathematica

PY - 1991

VL - 101

IS - 1

SP - 105

EP - 111

AB - We give an A_p type characterization for the pairs of weights (w,v) for which the maximal operator Mf(y) = sup 1/(b-a) ʃ_a^b |f(x)|dx, where the supremum is taken over all intervals [a,b] such that 0 ≤ a ≤ y ≤ b/ψ(b-a), is of weak type (p,p) with weights (w,v). Here ψ is a nonincreasing function such that ψ(0) = 1 and ψ(∞) = 0.

LA - eng

KW - weighted weak type inequalities; maximal functions

UR - http://eudml.org/doc/215889

ER -

## References

top- [C] C. P. Calderón, Some remarks on the multiple Weierstrass transform and Abel summability of multiple Fourier-Hermite Series, Studia Math. 32 (1969), 119-148. Zbl0182.15901
- [M1] B. Muckenhoupt, Poisson integrals for Hermite and Laguerre expansions, Trans. Amer. Math. Soc. 139 (1969), 231-242. Zbl0175.12602
- [M2] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, ibid. 165 (1972), 207-226. Zbl0236.26016

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