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On rough maximal operators and Marcinkiewicz integrals along submanifolds

100%

Al-Qassem H., Pan Y.

Studia Mathematica

2009

tom 190

nr 1

73-98

We investigate the $L^{p}$ boundedness for a class of parametric Marcinkiewicz integral operators associated to submanifolds and a class of related maximal operators under the $L(log L)^{α}(𝕊^{n-1})$ condition on the kernel functions. Our results improve and extend some known results.

Marcinkiewicz integrals on product spaces

81%

Al-Qassem H., Al-Salman A., Cheng L., Pan Y.

Studia Mathematica

2005

tom 167

nr 3

227-234

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.

Ograniczanie wyników

2 Studia Mathematica

2 Al-Qassem H.

2 Pan Y.

1 Al-Salman A.

1 Cheng L.

1 2009

1 2005

Wyniki wyszukiwania

On rough maximal operators and Marcinkiewicz integrals along submanifolds

Marcinkiewicz integrals on product spaces