FOR THE RELATIVISTIC SCHRÖDINGER OPERATOR (2009)
The Erwin, Schrödinger International Boltzmanngasse, I. E. Verbitsky, V. G. Maz’ya, I. E. Verbitsky
Abstract. We establish necessary and sufficient conditions for the boundedness of the relativistic Schrödinger operator H = √ − ∆ + Q from the Sobolev space W 1/2 2 (R n) to its dual W −1/2...
Form boundedness of the general second order differential operator (2004)
Maz'ya, V. G., Verbitsky, I. E.
We give explicit necessary and sufficient conditions for the boundedness of the general second order differential operator L with real- or complex-valued distributional coefficients acting from the...
Infinitesimal form boundedness and Trudinger's subordination for the Schr\"odinger operator (2004)
Maz'ya, V. G., Verbitsky, I. E.
We give explicit analytic criteria for two problems associated with the Schr\"odinger operator $H = -\Delta + Q$ on $L^2(\R^n)$ where $Q\in D'(\R^n)$ is an arbitrary real- or complex-valued...
Nonlinear potentials and two weight trace inequalities for general dyadic and radial kernels (2003)
Cascante, C., Ortega, J. M., Verbitsky, I. E.
We study trace inequalities of the type $$ \| T_k f\|_{L^q(d\mu)}\leq C \|f\|_{L^p(d\sigma)}, \qquad f \in L^p(d\sigma), $$ in the ``upper triangle case'' $1 \leq q
The form boundedness criterion for the relativistic Schr\"odinger operator (2003)
Maz'ya, V. G., Verbitsky, I. E.
We establish necessary and sufficient conditions for the boundedness of the relativistic Schr\"odinger operator $\mathcal{H} = \sqrt{-\Delta} + Q$ from the Sobolev space $W^{1/2}_2 (\R^n)$ to its...