TY  - JOUR
A1  - Weth, Tobias
A1  - Yeşil, Tolga
T1  - Fourier extension estimates for symmetric functions and applications to nonlinear Helmholtz equations
T2  - Annali di matematica pura ed applicata
N2  - We establish weighted Lp-Fourier extension estimates for O(N−k)×O(k)-invariant functions defined on the unit sphere SN−1, allowing for exponents p below the Stein–Tomas critical exponent 2(N+1)/N−1. Moreover, in the more general setting of an arbitrary closed subgroup G⊂O(N) and G-invariant functions, we study the implications of weighted Fourier extension estimates with regard to boundedness and nonvanishing properties of the corresponding weighted Helmholtz resolvent operator. Finally, we use these properties to derive new existence results for G-invariant solutions to the nonlinear Helmholtz equation −Δu−u = Q(x)|u|p−2u,u∈W2,p(RN), where Q is a nonnegative bounded and G-invariant weight function.
Y1  - 2021
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/63805
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-638052
SN  - 1618-1891
N1  - Open Access funding enabled and organized by Projekt DEAL.
N1  - T. Weth and T. Yeşil are supported by the German Science Foundation (DFG) within the project WE-2821/5-2.
VL  - 200.2021
IS  - 6
SP  - 2423
EP  - 2454
PB  - Springer
CY  - Berlin ; Heidelberg [u.a.]
ER  -