scholarly journals Partitions of Flat One-Variate Functions and a Fourier Restriction Theorem for Related Perturbations of the Hyperbolic Paraboloid

2021 ◽  
Author(s):  
Stefan Buschenhenke ◽  
Detlef Müller ◽  
Ana Vargas
Keyword(s):  
Hyperbolic Paraboloid ◽  
Restriction Theorem ◽  
Fourier Restriction

scholarly journals A Fourier restriction theorem for a perturbed hyperbolic paraboloid

2019 ◽  
Vol 120 (1) ◽  
pp. 124-154
Author(s):  
Stefan Buschenhenke ◽  
Detlef Müller ◽  
Ana Vargas
Keyword(s):  
Hyperbolic Paraboloid ◽  
Restriction Theorem ◽  
Fourier Restriction

A Restriction Theorem for a k-Surface in ℝn

2005 ◽  
Vol 48 (2) ◽  
pp. 260-266 ◽  
Author(s):  
Daniel M. Oberlin
Keyword(s):  
Restriction Theorem ◽  
Fourier Restriction ◽  
Restriction Estimate

AbstractWe establish a sharp Fourier restriction estimate for a measure on a k-surface in ℝn, where n = k(k + 3)/2.

On Fourier Restriction for Finite-Type Perturbations of the Hyperbolic Paraboloid

2021 ◽  
pp. 193-222
Author(s):  
Stefan Buschenhenke ◽  
Detlef Müller ◽  
Ana Vargas
Keyword(s):  
Finite Type ◽  
Hyperbolic Paraboloid ◽  
Fourier Restriction

scholarly journals Convolution Powers of Salem Measures With Applications

2017 ◽  
Vol 69 (02) ◽  
pp. 284-320 ◽  
Author(s):  
Xianghong Chen ◽  
Andreas Seeger
Keyword(s):  
Fourier Multipliers ◽  
Restriction Theorem ◽  
Fourier Restriction ◽  
Convolution Powers ◽  
Regularity Results

AbstractWe study the regularity of convolution powers for measures supported on Salemsets, and prove related results on Fourier restriction and Fourier multipliers. In particular we show that for α of the form d/n, n = 2, 3, … there exist α-Salem measures for which the L2Fourier restriction theorem holds in the range. The results rely on ideas of Körner. We extend some of his constructions to obtain upper regular α-Salem measures, with sharp regularity results forn-fold convolutions for all n ∈ ℕ.

How to Go beyond the Case hlin(φ‎) ≥ 5

2016 ◽  
Author(s):  
Isroil A. Ikromov ◽  
Detlef Müller
Keyword(s):  
Lower Bounds ◽  
The Other ◽  
Complex Interpolation ◽  
Restriction Theorem ◽  
Fourier Restriction

This chapter mostly considers the domains of type Dsubscript (l), which are in some sense “closest” to the principal root jet, since it turns out that the other domains Dsubscript (l) with l ≥ 2 are easier to handle. In a first step, by means of some lower bounds on the r-height, this chapter establishes favorable restriction estimates in most situations, with the exception of certain cases where m = 2 and B = 3 or B = 4. In some cases the chapter applies interpolation arguments in order to capture the endpoint estimates for p = psubscript c. Sometimes this can be achieved by means of a variant of the Fourier restriction theorem. However, in most of these cases the chapter applies complex interpolation in a similar way as has been done in Chapter 5.

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