Sharp Bounds and Plate Decomposition for the Cone Multipliers in Euclidean Space

Abstract

We give the restriction of the Fourier transform to a conical surface with the weak type estimates for cone multipliers on the Hardy space. We show sharp analysis and boundedness of Bergman projections on tube domains over light cones. We also show the bilinear approach to cone multipliers with some sharp bounds for the cone multiplier on negative order in The three related problems of Bergman spaces of certain tube domains over symmetric cones are considered. An improvements in Wolff's inequality and plate decompositions of cone multipliers are presented .