Hardy-littlewood maximal theorem

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August undefined, 2024

Webthe vector-valued extensions of the Hardy-Littlewood maximal theorem, the so-called Feﬀerman-Stein inequalities [12], has not been tackled. This is the main purpose of our paper. Let us ﬁrst recall these inequalities. Feﬀerman-Stein inequalities. Let 1 <+∞ and let (fn)n>1 be a sequence of measurable functions deﬁned on Rd. If P+∞ Web1930 A maximal theorem with function-theoretic applications. G. H. Hardy, J. E. Littlewood. Author Affiliations + Acta Math. 54: 81-116 (1930). DOI: 10.1007/BF02547518. ABOUT FIRST PAGE CITED BY ...

Remarks on the Hardy-Littlewood maximal function

WebJan 5, 2001 · thereby extending a theorem of Muckenhoupt from the scalar to the vector case. A basic chapter of the subject of singular integral operators is the weighted norm theory, which provides a necessary and su cient condition on a nonnegative function wfor such operators, and for the Hardy-Littlewood maximal function M, ikea wall shelving unit

THE HARDY–LITTLEWOOD MAXIMAL FUNCTION OF A …

WebJSTOR Home WebOct 1, 2006 · We will study the Hardy–Littlewood maximal function of a τ-measurable operator T .More precisely, letMbe a semi-finite von Neumann algebra with a normal … WebJun 5, 2024 · The Hardy–Littlewood theorem on a non-negative summable function. A theorem on integral properties of a certain function connected with the given one. ... ikea wall shelves with hooks

real analysis - Hardy-Littlewood maximal theorem …

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WebTheorem. (HardyLittlewood) For alla,RMa ≤ MRa. For example, with a as above, here are some relevant graphs: a Ma Ra RMa. Discrete HardyLittlewood 4 Ra MRa RMa MRa Proof. In several steps. ... Hardy and John E. Littlewood, ‘A maximal theorem with functiontheoretic applications’, Acta Mathematica54, 1930. WebMar 22, 2024 · In this paper, we define and study a canonical Hardy–Littlewood-type maximal operator associated with the one-dimensional generalized Fourier transform. For this operator to which covering methods do not apply, we construct a geometric maximal operator, which controls pointwise the canonical maximal operator, and for which we … is there tax on hats orono mnWebMar 6, 2024 · This is a corollary of the Hardy–Littlewood maximal inequality. Hardy–Littlewood maximal inequality. This theorem of G. H. Hardy and J. E. Littlewood states that M is bounded as a sublinear operator from the L p (R d) to itself for p > 1. That is, if f ∈ L p (R d) then the maximal function Mf is weak L 1-bounded and Mf ∈ L p (R d). ikea wall shelves uprights

"Webwhere the last inequality is a result of our result about the Hardy-Littlewood maximal func-tion. To nish, we solve p= ar. 2 Calderon-Zygmund We’re going to spend the next couple of classes talking about the Calderon-Zygmund theorem. First, let us consider the following theorem: Theorem 5. If u2C c 1(Rd), then for all 1 " - Hardy-littlewood maximal theorem

Hardy-littlewood maximal theorem

WebJan 20, 2016 · It is well known that the Hardy-Littlewood maximal function plays an important role in many parts of analysis. It is a classical mean operator, and it is … WebJan 1, 1982 · The Hardy-Littlewood maximal theorem is extended to functions of class PL in the sense of E. F. Beckenbach and T. RadÃƒÂ³, with a more precise expression of the absolute constant in the ...

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WebAug 24, 2024 · The Hardy-Littlewood maximal functions play an important role in harmonic analysis. Their boundness and sharp bounds are important since a variety of operators … Webtheorem is that the Hardy–Littlewood maximal operator is bounded in the Sobolev space W1,p(Rn)for1

WebAug 24, 2024 · The Hardy-Littlewood maximal functions play an important role in harmonic analysis. Their boundness and sharp bounds are important since a variety of operators are controlled by maximal functions. The and boundness of Hardy-Littlewood maximal functions are well-known [1–5]. However, sharp bounds are very hard to obtain. For a … <1, k@ i@ juk L p ...

WebUniversity of California, Berkeley WebBruna, J., Korenblum, B. On Kolmogorov's theorem, the Hardy-Littlewood maximal function and the radial maximal function. J. Anal. Math. 50, 225–239 (1988). …

WebMar 24, 2024 · Moreover, a simple modification of Kinnunen's arguments shows that the W 1,p -bound for the uncentered Hardy-Littlewood maximal operator M also holds (also see [8,Theorem 1]).

WebJun 21, 2015 · Hardy-Littlewood maximal theorem (Marcinkiewicz) Ask Question Asked 8 years, 10 months ago. Modified 7 years, 9 months ago. Viewed 780 times 1 … ikea wall storage hacksWebFeb 18, 2024 · The proof for the dyadic maximal operator is much shorter, but the same proof idea also works for the uncentered maximal operator. Also in this paper a part of the proof of Theorem 1.4 for the dyadic maximal operator is used also in the proof of Theorem 1.2 for the Hardy–Littlewood maximal operator. is there tax on gifts to childrenWebIn [5, Theorem 4.1.1] M, . de Guzman characterised the weak type (1,1) inequalities for maximal convolution operators in terms of finite sums of Dirac deltas. This discretisation … is there tax on groceries in ncWebSep 1, 2016 · The Hardy–Littlewood–Sobolev theorem for Riesz potential generated by Gegenbauer operator @article{Ibrahimov2016TheHT, title={The Hardy–Littlewood–Sobolev theorem for Riesz potential generated by Gegenbauer operator}, author={Elman J. Ibrahimov and Ali Akbulut}, journal={Transactions of A. … ikea wall storage systemsWebThe Hardy-Littlewood maximal operator and its variants, along with so-called square functions and singular integrals, form the central objects of study in har- ... one can give a quick proof of the Lebesgue di erentiation theorem that for almost every point, the value of an integrable function is the limit of in nitesimal averages taken about ... is there tax on holiday payWebThe boundedness of the Hardy–Littlewood maximal operator, ... We study the Hardy inequality and derive the maximal theorem of Hardy and Littlewood in the context of grand Lebesgue spaces, considered when the underlying measure space is the interval (0; 1) R, … Expand. 157. PDF. is there tax on gold salesWebthe uncentered maximal function, and later in [20] by Kurka for the centered Hardy-Littlewood maximal function. The latter proof turned out to be much more complicated. In [3], Aldaz and P erez L azaro improved Tanaka’s bound to the sharp krMfk L1(R) krfk L1(R) for the uncentered Hardy-Littlewood maximal function. is there tax on hats in nj