Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators

By Sanghyuk Lee. 2004

114 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d8c06231c22ffb8fd754f600839d934da82417b4

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

On plate decompositions of cone multipliers (2007, methodology): “.e. q≥ 2(d+1)/(d−1)). For the larger range q>2(d+2)/dthe proof of (3.9) is rather analogous to the proof of Proposition 2.3; one now uses Tao’s bilinear Fourier extension inequality [19] (see also [12] for related results). Unlike (2.11) in the conic case the inequality (3.9) is essentially optim”
A local smoothing estimate for the Schrödinger equation (2008, unknown): “When n 2, square function estimates (see [3,17,20]) yield ∥∥eit f ∥∥ Lq(Rn×[1,2]) Cq,α‖f ‖q,α”
Restriction and spectral multiplier theorems on asymptotically conic manifolds (2010, unknown): “For F = Fδ, part of region D is known for flat Euclidean space [25], and the celebrated BochnerRiesz conjecture is that, for flat Euclidean space, (1.”
Sharp estimates for oscillatory integral operators via polynomial partitioning (2017, result): “Lee [17] observed that under the positive-definite hypothesis H2`) one can establish improvements over the range given by Stein’s theorem in all dimensions.”
On the multilinear restriction and Kakeya conjectures (2005, background): “In recent years certain bilinear analogues of the restriction problem have come to light in natural ways from a number of sources (see for example [10], [19], [23], [31], [35], [28], [29], [32], [20], [14] concerning the well-posedness theory of non-linear dispersive equations, and applications to a”
Bilinear restriction estimates for surfaces with curvatures of different signs (2005, methodology): “This type of estimate was used not only for the restriction problem but it also has applications for a variety of related problems (see [14, 16] and references therein, and also [4, 7, 8, 9]).”
Linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces (2006, methodology): “This was used to derive linear estimates from bilinear ones (see [9,23,24]).”
Improved bounds for Stein's square functions (2010, methodology): “obtained by Carbery [3] in two dimensions and by the first author [22] in higher dimensions; however, as pointed out in [22], somewhat weaker estimates are already enough to bound the maximal function.”
Radial Fourier multipliers in high dimensions (2009, background): “[3], [1], [16], [2], [31], [19], and references in those papers) but no nice necessary and sufficient conditions have been known.”