330 research outputs found
Uniform resolvent estimates for Schr\"odinger operator with an inverse-square potential
We study the uniform resolvent estimates for Schr\"odinger operator with a
Hardy-type singular potential.
Let where is the usual Laplacian on
and where and
is a real function such that
the operator is a strictly positive
operator on . We prove some new uniform weighted
resolvent estimates and also obtain some uniform Sobolev estimates associated
with the operator .Comment: Comments are welcome.To appear in Journal of Functional Analysi
Linear adjoint restriction estimates for paraboloid
We prove a class of modified paraboloid restriction estimates with a loss of
angular derivatives for the full set of paraboloid restriction conjecture
indices. This result generalizes the paraboloid restriction estimate in radial
case from [Shao, Rev. Mat. Iberoam. 25(2009), 1127-1168], as well as the result
from [Miao et al. Proc. AMS 140(2012), 2091-2102]. As an application, we show a
local smoothing estimate for a solution of the linear Schr\"odinger equation
under the assumption that the initial datum has additional angular regularity.Comment: 24 page
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