Kakeya maximal function conjecture
WebbOn Stein’s Conjecture, we prove a conditional result: If the Lips-chitz Kakeya Maximal Function associated with vmaps is an estimate a little better than our L2 estimate, then the associated Hilbert trans-form is indeed bounded. Thus, the main question left open concerns the behavior of these novel Maximal Functions. Webbjugate exponent of p. Thus, Conjecture 1.1 would imply the Kakeya set conjecture, that Kakeya sets in Rn have Hausdorff dimension n; see, for instance, [5, 42, 28]. For n = …
Kakeya maximal function conjecture
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WebbKakeya operator conjecture ) Kakeya set conjecture Theorem The Kakeya maximal operator conjecture implies the Kakeya set conjecture. Proof (1/5). Minkowski: Let … Webb10 dec. 2009 · Preprint ], we establish optimal estimates for Kakeya sets and Kakeya maximal functions associated to algebraic varieties W over finite fields F. For …
WebbThen there is a conjecture for these functions that, if true, will imply the Kakeya set conjecture for higher dimensions: Kakeya maximal function conjecture: For all ε > 0, there exists a constant Cε> 0 such that for any function fand all δ … WebbA PROOF OF THE KAKEYA MAXIMAL FUNCTION CONJECTURE FROM A SPECIAL CASE Johan Aspegren Published 2024 Mathematics . First in this paper we will prove …
Webb1 jan. 2011 · Córdoba, A., The Kakeya maximal function and the spherical summation multipliers, Amer. J. Math. 99 (1977), 1–22. ... Recent progress on the Kakeya conjecture, Publicacions Matema-tiques, Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, U. Barcelona, 2002, pp. 161–180. Webbför 2 dagar sedan · This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author ...
Webb16 feb. 2001 · The Kakeya conjecture on local fields of positive characteristic Alejo Salvatore Mathematics Mathematika 2024 We state and prove an analogue of the Kakeya conjecture for the local field Fq ( (t))$\mathbb {F}_q (\! (t)\!)$ . This extends Arsovski's result on the Kakeya conjecture to local fields of positive… 1 PDF
Webbhold for p= (n+ 2)=2 (see [8]). A good survey of results relating to this conjecture was given by Katz and Tao and can be found in [6]. While the above gives the maximal function formulation of the Kakeya conjecture, a very common, discretized formulation deals with the overlap of tubes (neighborhoods of line segments). Suppose that huda kattan bornWebbConjecture. For every > 0 there exists a constant C > 0 so that kf∗ δ k q ≤ C 1 δ 2(n/p−1)+ kfk p for f ∈ Lp(Cn), 1 ≤ p ≤ n, q ≤ (n−1)p0. Despite the rather misleading terminology, … bielecki himalaistaWebbTHE KAKEYA SET AND MAXIMAL CONJECTURES FOR ALGEBRAIC VARIETIES OVER FINITE FIELDS JORDAN S. ELLENBERG, RICHARD OBERLIN, AND … bielorussia e kazakistanWebbIt's conjectured that K ( p, α) and N ( p, α) hold for all 1 ≤ p ≤ n and all α > 0, although this is not presently known. The idea here is that K ( p, α) and N ( p, α) give estimates for … huda kattan husband ethnicityWebb1 maj 2024 · A Proof of the Kakeya Maximal Function Conjecture from a Special Case. First in this paper we will prove the Kakeya maximal function conjecture in a special … bien 18-jul-20*asaWebbKakeya set conjecture. All Kakeya sets in Rn have Hausdor and Minkowski dimension n. Kakeya maximal operator conjecture. Let fT!g!2 be any collection of tubes of equal sizes and 1 eccentricity, whose orientation are -separated. Then for each >0 1! X!2 T j n n 1. X!2 jT!! n 1 n (1) Jean Burnazyan Kakeya maximal function conjecture huda hue vs ba ria vung tau fcWebb15 mars 2024 · Kakeya maximal function conjecture: For all ε > 0, there exists a constant Cε > 0 such that for any function f and all δ > 0, (see lp space for notation) … bien jouer au jass