Marcinkiewicz integrals on product spaces

• Autorzy: H. Al-Qassem , A. Al-Salman , L. C. Cheng , Y. Pan
• Języki publikacji: EN

Abstrakty

EN

We prove the $L^{p}$ boundedness of the Marcinkiewicz integral operators $μ_{Ω}$ on $ℝ^{n₁}× ⋯ ×ℝ^{n_{k}}$ under the condition that $Ω ∈ L(log L)^{k/2}(𝕊^{n₁-1}× ⋯ ×𝕊^{n_{k}-1})$. The exponent k/2 is the best possible. This answers an open question posed by Y. Ding.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 167
• Numer: 3
• Strony: 227-234

Daty

wydano

2005

Twórcy

autor

H. Al-Qassem

• Department of Mathematics, Yarmouk University, Irbid, Jordan

autor

A. Al-Salman

• Department of Mathematics, Yarmouk University, Irbid, Jordan

autor

L. C. Cheng

• Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, U.S.A.

autor

Y. Pan

• Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.

Identyfikatory

DOI

10.4064/sm167-3-4