Some Recent Progress on the Restriction Conjecture

Abstract

Abstract. We survey recent developments on the Restriction conjecture.

Weighted restriction type estimates for Grushin operators and application to spectral multipliers and Bochner–Riesz summability

“…when 0 < δ < . In this case, we cannot hope for (1−tL) [15], p. 420 and [16] for more details and recent progress on this problem.…”

A restriction theorem for the H-type groups

“…We refer the reader to [7] for the basic results on restriction theorems. Further developments can be found in [8] and the references therein. To generalize the restriction theorems to the Heisenberg group, D. Müller [5] investigated the restriction operator for the sublaplacian.…”

Restriction theory of the Selberg sieve, with applications

“…When the majorant β R enjoys additional Fourier or geometric properties it is often possible to recover estimates of HardyLittlewood majorant type. This is known as the restriction phenomenon and has been intensively studied in harmonic analysis; see for instance [32] for a recent survey of this theory.…”