Joonil Kim

On Mass Concentration for the L 2-Critical Nonlinear Schrödinger Equations

We consider the mass concentration phenomenon for the L 2-critical nonlinear Schrödinger equations. We show the mass concentration of blow-up solutions contained in space near the finite time. The new ingredient in this paper is a refinement of Strichartzs estimates with the mixed norm for 2 < q ≤ r.

Scattering Theory Below Energy for a Class of Hartree Type Equations

We prove the global existence and scattering for the Hartree-type equation in H s (ℝ3) the low regularity space s < 1. We follow the ideas in Colliander et al. (2004) to the Hartree-type nonlinearity, and also develop the theory of the classical multilinear operator modifying the L p estimate in Coifman and Meyer (1978).

Hilbert Transforms Along Curves in the Heisenberg Group

We consider Hilbert transforms along curves

Maximal Operators Associated with Vector Polynomials of Lacunary Coefficients

\Gamma

Multiparameter singular integrals and maximal operators along flat surfaces

on the Heisenberg group. In particular, necessary and sufficient conditions for the

Multiple-Hilbert transforms associated with polynomials

L^2

FRACTIONAL INTEGRAL ALONG HOMOGENEOUS CURVES IN THE HEISENBERG GROUP

-boundedness are given for

Singular Radon transforms along odd curves on the Heisenberg group

\Gamma(t)=(t,\gamma(t),0)

Ectopic bone formation associated with recombinant human bone morphogenetic proteins-2 using absorbable collagen sponge and beta tricalcium phosphate as carriers.

when

Atomic decomposition on Hardy-Sobolev spaces

\gamma