Hardy littlewood maximal operator
WebApr 10, 2024 · We study different geometric properties on infinite graphs, related to the weak-type boundedness of the Hardy–Littlewood maximal averaging operator. In … WebFeb 18, 2024 · The dyadic maximal operator has enjoyed a bit less attention than its continuous counterparts, such as the centered and the uncentered Hardy–Littlewood maximal operator. The dyadic maximal operator is different in the sense that formula ( 1.2 ) only holds for \(\alpha =0\) , \(p=1\) and only in the variation sense, for which formula ( …
Hardy littlewood maximal operator
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WebThen the Hardy-Littlewood maximal operator is bounded on Lp(x)(). Condition (1.4) is the natural analogue of (1.2) at in nity. It implies that there is some WebHere M is the Hardy–Littlewood maximal operator in ℝ n, Hα is the α-dimensional Hausdorff content, and the integrals are taken in the Choquet sense. The Choquet integral of ϕ [ges ]0 with respect to a set function C is defined by formula here Precise definitions of M and Hα will be given below.
WebHardy-Littlewood maximal inequality asserts that they are also uniformly bounded in shape: Proposition 1.1 (Hardy-Littlewood maximal inequality). We have ksup r>0 Arf … WebOct 3, 2014 · The main aim of this paper is to introduce an appropriate dyadic one-sided maximal operator , smaller than the one-sided Hardy–Littlewood maximal operator M+ but such that it controls M+ in a similar way to how the usual dyadic maximal operator controls the Hardy-Littlewood maximal operator.
In mathematics, the Hardy–Littlewood maximal operator M is a significant non-linear operator used in real analysis and harmonic analysis. The operator takes a locally integrable function f : R → C and returns another function Mf. For any point x ∈ R , the function Mf returns the maximum of a set of reals, namely the set … See more This theorem of G. H. Hardy and J. E. Littlewood states that M is bounded as a sublinear operator from the L (R ) to itself for p > 1. That is, if f ∈ L (R ) then the maximal function Mf is weak L -bounded and Mf ∈ L (R ). Before stating … See more It is still unknown what the smallest constants Cp,d and Cd are in the above inequalities. However, a result of Elias Stein about spherical maximal functions can be used to show that, for 1 < p < ∞, we can remove the dependence of Cp,d on the dimension, … See more While there are several proofs of this theorem, a common one is given below: For p = ∞, the inequality is trivial (since the average of a function is no larger than its essential supremum). … See more • Rising sun lemma See more WebJul 1, 1995 · A characterization is obtained for weight functions V for which the Hardy-Littlewood maximal operator is bounded from l1I'(R", wdttx) to 1I)(Rfl, vd.'V) for sonme nontrivial wv. In this note we … Expand
WebApr 1, 2004 · We consider Hardy-Littlewood maximal operator on the general Lebesgue space L-p(x)(R-n) with variable exponent. A sufficient condition on the function p is known for the boundedness of the maximal ...
WebNov 14, 2011 · THE HARDY–LITTLEWOOD MAXIMAL FUNCTION AND WEIGHTED LORENTZ SPACES MARÍA J. CARRO and JAVIER SORIA Journal of the London Mathematical Society Published online: 1 February 1997 Article Maximal Operators and Cantor Sets Kathryn E. Hare Canadian Mathematical Bulletin Published online: 20 … scan shipping inc trackingWebNov 15, 2024 · In [ 9 ], Ombrosi, Rivera-Ríos, and Safe have proved a sharp analog of Fefferman-Stein inequality for the Hardy–Littlewood maximal operator on the infinite rooted k -ary tree and subsequently in [ 8 ], weighted inequalities for the Hardy–Littlewood maximal function were investigated by Ombrosi and Rivera-Ríos. scan-shipping trackingWebHardy-Littlewood maximal operator on L^p (x) (ℝ) A. Nekvinda Published 2004 Mathematics Mathematical Inequalities & Applications View via Publisher files.ele … scan shipping californiaWebTHE HARDY-LITTLEWOOD MAXIMAL OPERATOR 215 which is a contradiction. Thus, the sequence {Ek) is a covering of {x: Mf(x) < oo}. On the other hand, on account of the weak type (1,1) boundedness of the Hardy-Littlewood maximal function operator, the set {x: Mf(x) = 00} is of mea-sure zero and therefore (2.6) is proved. scan shonen jumpWebThe sharp estimates of the m-linear p-adic Hardy and Hardy-Littlewood-Polya operators on Lebesgue spaces with power weights are obtained in this paper. ... HARDY-LITTLEWOOD-POLYA INEQUALITY FOR A LINEAR DIFFERENTIAL OPERATOR AND SOME RELATED OPTIMAL PROBLEMS [J] ... Sharp estimates for dyadic-type maximal operators and … ruchelman pllcWeb1 Consider the centered Hardy_littlewood maximal operator M f ( x) := sup r > 0 1 B ( x, r) ∫ B ( x, r) f ( y) d y and the uncentered M f ( x) := sup r > 0, y − x < r 1 B ( y, r) ∫ … ruchelman cruikshankWebApr 23, 2024 · For a function , the Hardy–Littlewood maximal operator on G is defined as. If G has vertices, the maximal operator can be rewritten by. Over the last several years … ruchelman law firm