Related papers: On the Schrodinger maximal function in higher dime…
We construct explicit integral relations between propagators of generalized Schr\"odinger equations that are linked by higher-order supersymmetry. Our results complement and extend the findings obtained in J. Phys.A 40, 10557 (2007) for the…
We study the boundedness of commutators of the Hardy-Littlewood maximal function and the sharp maximal function on weighted Morrey spaces when the symbols of the commutators belong to weighted Lipschitz spaces. Some new characterizations…
A long standing conjecture for the linear Schroedinger equation states that 1/4 of derivative in $L^2$, in the sense of Sobolev spaces, suffices in any dimension for the solution to that equation to converge almost everywhere to the initial…
It is proved that when solving Schroedinger equations for radially symmetric potentials the effect of higher dimensions on the radial wave function is equivalent to the effect of higher angular momenta in lower dimensional cases. This…
In this paper, we present a different proof on the discrete Fourier restriction. The proof recovers Bourgain's level set result on Strichartz estimates associated with Schr\"odinger equations on torus. Some sharp estimates on…
We present an alternative way to recover the recent result from \cite{LR} using the pseudoconformal transformation.
We describe a certain "self-similar" family of solutions to the free Schroedinger equation in all dimensions, and derive some consequences of such solutions for two specific problems.
A formulation of the Carleson embedding theorem in the multilinear setting is proved which allows to obtain a multilinear analogue of Sawyer's two weight theorem for the multisublinear maximal function \mathcal{M} introduced in Lerner et…
Under the assumption that orthogonal polynomials of several variables admit an addition formula, we can define a convolution structure and use it to study the Fourier orthogonal expansions on a homogeneous space. We define a maximal…
In this paper, we investigate the weighted multilinear boundedness properties of the maximal higher order Calder\'on commutator for the dimensions larger than two. We establish all weighted multilinear estimates on the product of the…
Relation between one-dimensional Schroedinger equation and the vacuum eigenvalues of the Q-operators is extended to their higher-level eigenvalues.
We provide a new proof for maximal monotonicity of the subdifferential of a convex function.
In this note we use recent results concerning the sum theorem for maximal monotone multifunctions in general Banach spaces to find new characterizations and properties of regular maximal monotone multifunctions and then use these to…
This article is devoted to some foundational questions of resurgent analysis as applied to the Schr\"odinger equation in one dimension.
We prove some Sawyer-type characterizations for multilinear fractional maximal function for the upper triangle case. We also provide some two-weight norm estimates for this operator. As one of the main tools, we use an extension of the…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
We obtain boundedness for the bilinear spherical maximal function in a range of exponents that includes the Banach triangle and a range of $L^p$ with $p<1$. We also obtain counterexamples that are asymptotically optimal with our positive…
We review recent progress in gauging maximal supergravity theories
We prove (essentially) sharp $L^4$ level set estimates for the periodic Schr\"odinger maximal operator in a certain range of the cut-off parameter.
In this note we present an algorithm to generate new Schr\" odinger type equations explicitly solvable in terms of orthogonal polynomials or associated special functions.