Weak-type inequalities for maximal operators acting on Lorentz spaces

Adam Osękowski

Adam Osękowski

Banach Center Publications, Tome 102 (2014), p. 145-162 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove sharp a priori estimates for the distribution function of the dyadic maximal function ℳ ϕ, when ϕ belongs to the Lorentz space $L^{p, q}$ , 1 < p < ∞, 1 ≤ q < ∞. The approach rests on a precise evaluation of the Bellman function corresponding to the problem. As an application, we establish refined weak-type estimates for the dyadic maximal operator: for p,q as above and r ∈ [1,p], we determine the best constant $C_{p, q, r}$ such that for any $ϕ \in L^{p, q}$ , ${| | ℳ ϕ | |}_{r, \infty} \leq C_{p, q, r} {| | ϕ | |}_{p, q}$ .

Publié le : 2014-01-01

Zbl 1293.42023

EUDML-ID : urn:eudml:doc:281906

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     author = {Adam Os\k ekowski},
     title = {Weak-type inequalities for maximal operators acting on Lorentz spaces},
     journal = {Banach Center Publications},
     volume = {102},
     year = {2014},
     pages = {145-162},
     zbl = {1293.42023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc101-0-12}
}

Adam Osękowski. Weak-type inequalities for maximal operators acting on Lorentz spaces. Banach Center Publications, Tome 102 (2014) pp. 145-162. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc101-0-12/