A weak type estimate for rough singular integrals
نویسندگان
چکیده
منابع مشابه
A Weak Type Estimate for Rough Singular Integrals
We obtain a weak type (1, 1) estimate for a maximal operator associated with the classical rough homogeneous singular integrals TΩ. In particular, this provides a different approach to a sparse domination for TΩ obtained recently by Conde-Alonso, Culiuc, Di Plinio and Ou [5].
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نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.
15 صفحه اولWeighted estimates for rough oscillatory singular integrals
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
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Weighted norm inequalities are proved for a rough homogeneous singular integral operator and its corresponding maximal truncated singular operator. Our results are essential improvements as well as extensions of some known results on the weighted boundedness of singular integrals.
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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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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2019
ISSN: 0213-2230
DOI: 10.4171/rmi/1094