On rough maximal operators and Marcinkiewicz integrals along submanifolds
نویسندگان
چکیده
منابع مشابه
Rough Marcinkiewicz Integrals On Product Spaces
In this paper, we establish an Lp boundedness result of a class of Marcinkiewicz integral operators on product domains with rough kernels.
متن کاملRough Marcinkiewicz Integral Operators
We study the Marcinkiewicz integral operator M f(x) = ( ∫∞ −∞ | ∫ |y|≤2t f (x − (y))(Ω(y)/|y|n−1)dy|2dt/22t)1/2, where is a polynomial mapping from Rn into Rd and Ω is a homogeneous function of degree zero on Rn with mean value zero over the unit sphere Sn−1. We prove an Lp boundedness result of M for rough Ω. 2000 Mathematics Subject Classification. 42B20, 42B15, 42B25.
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Stein proved that ifΩ∈ Lipα(Sn−1), (0<α≤ 1), then μΩ is bounded on Lp for all 1<p ≤ 2 [18]. Since then, the study of the Lp boundedness of μΩ under various conditions on the function Ω has attracted the attention of many authors ([1, 4, 5, 7, 10, 13], among others). In particular, Chen et al. in [8] studied the Lp boundedness of μΩ under the following condition on the function Ω which was intro...
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We establish the L boundedness of singular integrals on product domains with rough kernels in L(logL) and are supported by subvarieties.
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2009
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm190-1-3