Littlewood–Paley–Rubio de Francia inequality for the Walsh system
نویسندگان
چکیده
منابع مشابه
Dedicated to the Memory of Jose Luis Rubio De Francia
In this paperwe prove that the /~.,-cube can be (1 + s)-embedded into any 1 -subsyntmetrie C(s>n.dimensional normed space. Marcus and Pisier in [5]iniciated tite study of tite geometry ob finite metric spaces. Bourgain, Milman and Wolbson introduced a new notion of metnc type and developed tite non-linear titeory of Banacit spaces (see [2]and [7]). AII titese themes have been studied more inten...
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Given a compact connected abelian group G, its dual group Γ can be ordered (in a non-canonical way) so that it becomes an ordered group. It is known that, for any such ordering on Γ and p in the range 1 < p < ∞, the characteristic function χI of an interval I in Γ is a p−multiplier with a uniform bound (independent of I) on the corresponding operator SI on Lp(G). In this note it is shown that, ...
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Let Lk denote the Lebesgue constants of the Walsh system. The following exact result is established by means of Mellin transforms: ∑ 1≤k<n Lk = n 4 log2 n+ nF (log2 n)− Ln 2 , for n ≥ 1, where F (u) is a continuous periodic function with period 1 whose Fourier coefficients can be explicitly expressed in terms of Riemann’s zeta function. This improves an old result of Fine.
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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 اولThe Littlewood–paley–rubio De Francia Property of a Banach Space for the Case of Equal Intervals
are well known. When {Ij}j∈Z is the collection of dyadic intervals, i.e., I0 = {0} and Ij = sgn(j)[2 , 2) for |j| > 0, the estimate (1.2) is the classical Littlewood–Paley inequality which is valid (as well as the reverse estimate with ≥ in place of ≤) for all p ∈ (1,∞). If the Ij are disjoint intervals of equal length, then (1.2) holds if and only if p ∈ [2,∞); this was first proved by L. Carl...
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ژورنال
عنوان ژورنال: St. Petersburg Mathematical Journal
سال: 2017
ISSN: 1061-0022,1547-7371
DOI: 10.1090/spmj/1469