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Boundedness of rough integral operators on Triebel-Lizorkin spaces. (English) Zbl 1301.42021

The authors investigate the boundedness of three types of singular integrals operators in homogeneous Triebel-Lizorkin spaces. The following types of operators are considered:
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homogeneous Calderon-Zygmund operators with rough kernels,
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a certain class of oscillatory singular integral operators,
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Marcinkiewicz operators.
The authors improve and generalize the earlier results in particular by L. Grafakos and A. Stefanov [Indiana Univ. Math. J. 47, No. 2, 455–469 (1998; Zbl 0913.42014)], Y. Chen and Y. Ding [J. Math. Anal. Appl. 347, No. 2, 493–501 (2008; Zbl 1257.42021)], D. Fan and Y. Pan [Am. J. Math. 119, No. 4, 799–839 (1997; Zbl 0899.42002)].

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
42B25 Maximal functions, Littlewood-Paley theory
42B35 Function spaces arising in harmonic analysis
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References:

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