Marcinkiewicz integrals on product spaces

H. Al-Qassem; A. Al-Salman; L. C. Cheng; Y. Pan

H. Al-Qassem ; A. Al-Salman ; L. C. Cheng ; Y. Pan

Studia Mathematica, Tome 166 (2005), p. 227-234 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove the $L^{p}$ boundedness of the Marcinkiewicz integral operators $μ_{Ω}$ on $ℝ^{n ₁} \times \dots \times ℝ^{n_{k}}$ under the condition that $Ω \in L {(l o g L)}^{k / 2} (^{n ₁ - 1} \times \dots \times^{n_{k} - 1})$ . The exponent k/2 is the best possible. This answers an open question posed by Y. Ding.

Publié le : 2005-01-01

Zbl 1084.42008

EUDML-ID : urn:eudml:doc:284761

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     title = {Marcinkiewicz integrals on product spaces},
     journal = {Studia Mathematica},
     volume = {166},
     year = {2005},
     pages = {227-234},
     zbl = {1084.42008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm167-3-4}
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H. Al-Qassem; A. Al-Salman; L. C. Cheng; Y. Pan. Marcinkiewicz integrals on product spaces. Studia Mathematica, Tome 166 (2005) pp. 227-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm167-3-4/