TY - JOUR
T1 - Transference of local to global L2 maximal estimates for dispersive partial differential equations
AU - Castro, Alejandro J.
AU - Rodríguez-López, Salvador
AU - Staubach, Wolfgang
PY - 2019/3
Y1 - 2019/3
N2 - In this paper we give an elementary proof for transference of local to global maximal estimates for dispersive PDEs. This is done by transferring local L2 estimates for certain oscillatory integrals with rough phase functions, to the corresponding global estimates. The elementary feature of our approach is that it entirely avoids the use of the wave packet techniques which are quite common in this context, and instead is based on scalings and classical oscillatory integral estimates.
AB - In this paper we give an elementary proof for transference of local to global maximal estimates for dispersive PDEs. This is done by transferring local L2 estimates for certain oscillatory integrals with rough phase functions, to the corresponding global estimates. The elementary feature of our approach is that it entirely avoids the use of the wave packet techniques which are quite common in this context, and instead is based on scalings and classical oscillatory integral estimates.
KW - Dispersive equations
KW - Maximal-function estimates
KW - Oscillatory integrals
KW - Schrödinger equation
UR - http://www.scopus.com/inward/record.url?scp=85055736001&partnerID=8YFLogxK
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U2 - 10.1016/j.jmaa.2018.10.082
DO - 10.1016/j.jmaa.2018.10.082
M3 - Article
AN - SCOPUS:85055736001
VL - 471
SP - 411
EP - 422
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1-2
ER -