Spherical maximal function

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August undefined, 2024

Webus to consider functions on Zd and obtaining a wide range of estimates. Our range is not sharp, but approaches sharp estimates as dÑ8. We relate some necessary conditions of … WebFeb 28, 2024 · ENDPOINT MAPPING PROPERTIES OF SPHERICAL MAXIMAL OPERATORS A. Seeger, T. Tao, James Wright Mathematics Journal of the Institute of Mathematics of Jussieu 2003 For a function $f\in L^p (\mathbb {R}d)$, $d\ge 2$, let $A_tf (x)$ be the mean of $f$ over the sphere of radius $t$ centred at $x$.

Spherical maximal functions and fractal dimensions of dilation sets

The main results of this paper are the boundedness of the spherical maximal function, the maximal Bochner–Riesz mean, the geometrical maximal functions and the minimal function on Herz spaces with variable exponents. The classical Herz space was introduced in to study the Fourier series. See more The spherical maximal function [47, 48] is defined as where S^{n-1} is the unit sphere on {{\mathbb {R}}}^{n} and \mu is the normalized surface measure on S^{n-1}. The weighted norm … See more We only present the proof for {K}^{\alpha (\cdot )}_{p(\cdot ),q} as the proof for {\dot{K}}^{\alpha (\cdot )}_{p(\cdot ),q}follows from some simple modifications. Take \delta =\frac{n-2}{n-1}. Since p_{-}, p_{+}, … See more Let \frac{n}{n-1} WebMar 15, 2012 · We use simple one-dimensional operators to bound pointwise the spherical maximal operator acting on radial functions. With this bounds we obtain weighted … diy bathroom linoleum

Maximal functions: Spherical means. Semantic Scholar

Web8 CHAPTER 1. SPHERICAL HARMONICS Therefore, the eigenfunctions of the Laplacian on S1 are the restrictions of the harmonic polynomials on R 2to S 1and we have a Hilbert sum decomposition, L(S) = L 1 k=0 H k(S 1). It turns out that this phenomenon generalizes to the sphere S n R +1 for all n 1. Let us take a look at next case, n= 2. WebFeb 12, 2024 · In this paper, the mapping properties of the spherical maximal function, the fractional maximal functions, the variation and oscillation operators for Riesz transform … WebSpherical Maximal Operators on Radial Functions. A. Seeger, S. Wainger, James Wright. Mathematics. 1996. Let Atf (x) denote the mean of f over a sphere of radius t and center … crafty projects for adults

Sparse bounds for spherical maximal functions - Semantic Scholar

WebBILINEAR SPHERICAL MAXIMAL FUNCTION arXiv:1704.03586v1 [math.CA] 12 Apr 2024 J. A. BARRIONEVO, LOUKAS GRAFAKOS, DANQING HE, PETR HONZÍK, AND LUCAS … WebBOUNDS FOR SPHERICAL MAXIMAL OPERATORS T. Anderson, Kevin A. Hughes, J. Roos, A. Seeger Mathematics 2024 Let f ∈ L (R), d ≥ 3, and let Atf (x) the average of f over the sphere with radius t centered at x. For a subset E of [1, 2] we prove close to sharp L → L estimates for the maximal function supt∈E Atf… Expand 1 Highly Influenced crafty prospectorWebBILINEAR SPHERICAL MAXIMAL FUNCTION arXiv:1704.03586v1 [math.CA] 12 Apr 2024 J. A. BARRIONEVO, LOUKAS GRAFAKOS, DANQING HE, PETR HONZÍK, AND LUCAS OLIVEIRA A BSTRACT. We obtain boundedness for the bilinear spherical maximal function in a range of exponents that includes the Banach triangle and a range of L p with p < 1. We also obtain ... crafty products

"WebTHE DISCRETE SPHERICAL MAXIMAL FUNCTION: A NEW PROOF OF ‘2-BOUNDEDNESS NEIL LYALL AKOS MAGYAR ALEX NEWMAN PETER WOOLFITT Abstract. We provide a … " - Spherical maximal function

Spherical maximal function

WebAug 20, 2003 · The discrete spherical maximal function is defined as the operator A( (f)(n) = supN1 f(n A~cc?, s~~ C f(7mIr where f: Zd -- C is a function, d > 2, Nd(r) denotes the … WebAnswer: What is the maximum and minimum value of ϕ in spherical polar coordinates? You need to define the ϕ in your question. If it relates to latitude, then the minimum and …

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WebSep 13, 2024 · The main objective of this paper is the spherical maximal function on finite graphs. Let us introduce one definition. Definition 1.2 (Spherical maximal operator on … WebAbstract: In dimensions n ≥ 2 we obtain L p 1 ( R n) × ⋯ × L p m ( R n) to L p ( R n) boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide counterexamples that indicate the optimality of our results.

WebMay 17, 2013 · The spherical maximal function was introduced by Stein in [37]. The mapping properties of the spherical maximal function on the weighted Lebesgue spaces, the radial Lebesgue spaces and the... WebApr 12, 2024 · Tengda Han · Max Bain · Arsha Nagrani · Gul Varol · Weidi Xie · Andrew Zisserman ... Volume Rendering of Signed Ray Distance Functions for Generalizable Multi-View Reconstruction ... Balanced Spherical Grid for Egocentric View Synthesis Changwoon Choi · Sang Min Kim · Young Min Kim

WebThe maximal spherical function si is the maximal function associated to the convolution operator with the measure μ (see (1)). The aim of this paper is to establish Lp-inequalities for si. Let M denote the standard maximal function, i.e. the maximal function associated to the characteristic function of the unit homogeneous ball B\ := {n € Nv ... <\infty. If \omega ^{\frac{n-1}{n-2}}\in A_{1}, then there is a constant C>0 such that See more Let n\ge 2, 0<\infty, p(\cdot )\in C^{\log }({\mathbb {R}}^{n}) with 1

WebSPHERICAL MAXIMAL OPERATORS ON RADIAL FUNCTIONS Andreas Seeger, Stephen Wainger and James Wright 1. Introduction For a function f ∈ Lp(Rd) we deﬁne the …

WebApr 14, 2024 · 640:135 - Calculus I ; 640:151-152 - Calculus I for the Mathematical and Physical Sciences ; 640:311:H1 - Introduction to Real Analysis I diy bathroom linen towerWebWe address the discrete lacunary spherical maximal function. We say that a set of integers f 2 k: k 1gis lacunary if 2 k+1 2 2 k for all k2N. Let A lac = sup k2Z A k f. We will see that the … diy bathroom lighting ideasWebdomination bounds for a related global spherical maximal function. 1.Introduction and statement of results Let A tf(x) denote the mean of a locally integrable function fover the sphere with radius tcentered at x. That is, A tf(x) = Z f(x ty)d˙(y); where ˙is the standard normalized surface measure on the unit sphere in Rdand d 2. Let Eˆ[1;2 ... craftypupsWebApr 2, 2011 · is easy to prove, see [5], [6], that actually the spherical maximal operator is bounded in the Sobolev spaces S: W1;p!W1;pfor all n=(n 1) craftypumWebMar 12, 2024 · For specific functions (such as the famous Hardy–Littlewood maximal function), the measurability can be proved directly (in this case, one observes that it suffices to take rational t ). In general, I need the measurability of the following type of maximal functions (as is used later in the book): Let ϕ ∈ L 1 ( R n) such that ∫ ϕ = 1. crafty pug worldWebApr 2, 2011 · The case of the spherical maximal function has also been discussed in [8]. As a corollary of Theorem 1.1 we will prove Proposition 1.2. If the claim of Theorem 1.1 is true for 1 crafty projectsWebSPHERICAL MAXIMAL FUNCTIONS AND FRACTAL DIMENSIONS OF DILATION SETS JORIS ROOS ANDREAS SEEGER Abstract. For the spherical mean operators At in Rd, d≥ 2, we … diy bathroom medicine cabinet ideas