Sharp Logarithmic Inequalities for Two Hardy-type Operators
Adam Osękowski
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015), p. 237-247 / Harvested from The Polish Digital Mathematics Library
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For any locally integrable f on ℝⁿ, we consider the operators S and T which average f over balls of radius |x| and center 0 and x, respectively: Sf(x)=1/|B(0,|x|)|∫B(0,|x|)f(t)dt, Tf(x)=1/|B(x,|x|)|∫B(x,|x|)f(t)dt for x ∈ ℝⁿ. The purpose of the paper is to establish sharp localized LlogL estimates for S and T. The proof rests on a corresponding one-weight estimate for a martingale maximal function, a result which is of independent interest.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:281161 
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     author = {Adam Os\k ekowski},
     title = {Sharp Logarithmic Inequalities for Two Hardy-type Operators},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     volume = {63},
     year = {2015},
     pages = {237-247},
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     language = {en},
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Adam Osękowski. Sharp Logarithmic Inequalities for Two Hardy-type Operators. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) pp. 237-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba8039-12-2015/