Local smoothing type estimates on Lp for large p

By T. Wolff. 2000

214 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f16371a36766bcf3b2607cda2013541217aa2aa6

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In Applied Mathematics

In Mathematical Physics

In Numerical Analysis

Citations in the corpus

A local smoothing estimate in higher dimensions (2002, methodology): “The purpose of this paper is to prove the higher-dimensional analogue of the local smoothing estimate of [ 10 ].”
L p regularity of averages over curves and bounds for associated maximal operators (2005, methodology): “A counterexample in [ 22 ] shows that this inequality cannot hold for all e> 0i f p 22 ].”
The proof of the l 2 Decoupling Conjecture (2015, background): “We point out that Wolﬀ [36] has initiated the study of l p decouplings, p > 2 in the case of the cone.”
Radial Fourier multipliers in high dimensions (2009, background): “[3], [1], [14], [2], [ 26 ], [16], and references in those papers) but no nice necessary and sufficient conditions have been known.”
Recent progress on the Kakeya conjecture (2000, background): “We will focus on the standard Kakeya problem for line segments and not discuss other important variants (such as Kakeya estimates for circles, light rays, or k-planes; see e.g. [22], [26], [ 27 ], [9]).”
Linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces (2006, result): “|) it is easy to verify that the condition on μ is sharp (see [23]) and some sharp Lp-local smoothing estimates were obtained by Wolff [28] in R3, and Łaba and Wolff [8] in higher dimensions.”
A sharp square function estimate for the cone in ℝ3 (2019, background): “In [25], Wolff proved the local smoothing conjecture for p > 74 in the full range of α.”
On plate decompositions of cone multipliers (2007, methodology): “In his fundamental work [22], Wolff developed a method to prove such inequalities for large values of p, and obtained a positive answer for d = 2 and p > 74.”
Littlewood–Paley Decompositions Related to Symmetric Cones and Bergman Projections in Tube Domains (2004, background): “In particular, we establish a link between our problem and WolL’s conjecture for k kp;mic-norms (see [17, 12]).”