A note on maximal singular integrals with rough kernels
نویسندگان
چکیده
منابع مشابه
L Bounds for Singular Integrals and Maximal Singular Integrals with Rough Kernels
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 show that the L(w) operator norm of the composition M◦TΩ, where M is the maximal operator and TΩ is a rough homogeneous singular integral with angular part Ω ∈ L∞(Sn−1), depends quadratically on [w]A2 , and this dependence is sharp.
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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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It is shown that maximal truncations of nonconvolution L-bounded singular integral operators with kernels satisfying Hörmander’s condition are weak type (1, 1) and L bounded for 1 < p < ∞. Under stronger smoothness conditions, such estimates can be obtained using a generalization of Cotlar’s inequality. This inequality is not applicable here and the point of this article is to treat the bounded...
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Weighted norm inequalities for maximal truncated operators of multilinear singular integrals with non-smooth kernels in the sense of Duong, Grafakos, and Yan are obtained; this class of operators extends the class of multilinear CalderónZygmund operators introduced by Coifman and Meyer and includes the higher order commutators of Calderón. The weighted norm inequalities obtained in this work ar...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2020
ISSN: 1029-242X
DOI: 10.1186/s13660-020-02504-8