On some inequalities of Bourgain, Brezis, Maz'ya, and Shaposhnikova related to $L^1$ vector fields

This class K L contains almost all fundamental operators (we refer the reader to [32] for the classical case L = − ∆) related to the Schr¨odinger operator

The approximation Ansatz proposed here is a tool to compute approximations of the exact solution to the Cauchy problem (1)–(2) and yields a representation of these so- lution by

Since in this case the actual 3-D microstructure of the bulk of the sample was not known, a 3-D unit cell was built assuming a randomly-generated distribution of bulk

This class K contains almost all important operators in harmonic analysis: Calder´on-Zygmund type operators, strongly singular integral operators, multiplier

Titchmarsh’s [5, Therem 85] characterized the set of functions in L 2 ( R ) satisfying the Cauchy Lipschitz condition by means of an asymptotic estimate growth of the norm of

understanding of the wave operators has been necessary, and it is during such investigations that several integral operators or singular integral operators have appeared, and that

The problems involve the square roots of the second order non Fredholm differential operators and we use the methods of spectral and scattering theory for Schr¨odinger type

The space D k p of differential operators of order ≤ k, from the differen- tial forms of degree p of a smooth manifold M into the functions of M, is a module over the Lie algebra