Singular integrals with rough kernels along real-analytic submanifolds in ${\mathbf {R}}^3$
نویسندگان
چکیده
منابع مشابه
Rough Singular Integrals Along Submanifolds of Finite Type on Product Domains
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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Convolution type Calderón-Zygmund singular integral operators with rough kernels p.v. Ω(x)/|x| are studied. A condition on Ω implying that the corresponding singular integrals and maximal singular integrals map L → L for 1 < p < ∞ is obtained. This condition is shown to be different from the condition Ω ∈ H1(Sn−1).
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We prove optimal bounds in L2(R2) for the maximal operator obtained by taking a singular integral along N arbitrary directions in the plane. We also give a new proof for the optimal L2 bound for the single scale Kakeya maximal function in the plane.
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Sn−1 Ω = 0. The radial factor h has bounded variation. The necessary condition on the weight is similar to the Ap condition but involves rectangles (instead of cubes) arising from a covering of a star-shaped set related to Ω. AMS Mathematics Subject Classification: 42B20
متن کاملRough singular integrals on product spaces
where, p.v. denotes the principal value. It is known that if Φ is of finite type at 0 (see Definition 2.2) and Ω ∈ 1(Sn−1), then TΦ,Ω is bounded on Lp for 1<p <∞ [15]. Moreover, it is known that TΦ,Ω may fail to be bounded on Lp for any p if the finite-type condition is removed. In [8], Fan et al. showed that the Lp boundedness of the operator TΦ,Ω still holds if the condition Ω ∈ 1(Sn−1) is re...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2002
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-02-03175-6