Let Gamma be a smooth compact convex planar curve with are length dm and let d sigma = psi dm where psi is a cutoff function. For Theta is an element of SO(2) set sigma (Theta)(E) = sigma(ThetaE) for any measurable planar set E. Then. for suitable functions f in R-2, the inequality {integral (SO(2)) [integral (R2) /(f) over cap(xi)/(2) d sigma (Theta)(xi)](s/2) d Theta}(1/s) less than or equal to c \\f\\(p) represents an average over rotations, of the Stein-Tomas restriction phenomenon. We obtain best possible indices for the above inequality when Gamma is any convex curve and under various geometric assumptions.
Brandolini, L., Iosevich, A., Travaglini, G. (2001). Spherical means and the restriction phenomenon. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 7(4), 359-372 [10.1007/BF02514502].
Spherical means and the restriction phenomenon
TRAVAGLINI, GIANCARLO
2001
Abstract
Let Gamma be a smooth compact convex planar curve with are length dm and let d sigma = psi dm where psi is a cutoff function. For Theta is an element of SO(2) set sigma (Theta)(E) = sigma(ThetaE) for any measurable planar set E. Then. for suitable functions f in R-2, the inequality {integral (SO(2)) [integral (R2) /(f) over cap(xi)/(2) d sigma (Theta)(xi)](s/2) d Theta}(1/s) less than or equal to c \\f\\(p) represents an average over rotations, of the Stein-Tomas restriction phenomenon. We obtain best possible indices for the above inequality when Gamma is any convex curve and under various geometric assumptions.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
