Lp-theory of type 1, 1-operators

Fundamental Results for Pseudo-Differential Operators of Type 1, 1

Abstract: This paper develops some deeper consequences of an extended definition, proposed previously by the author, of pseudo-differential operators that are of type 1, 1 in Hörmander’s sense. Thus, it contributes to the long-standing problem of creating a systematic theory of such operators. It is shown that type 1, 1-operators are defined and continuous on the full space of temperate distrib...

Cohomology of aff(1|1) acting on the space of bilinear differential operators on the superspace IR1|1

We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.

Lp SPECTRAL THEORY OF HIGHER-ORDER ELLIPTIC DIFFERENTIAL OPERATORS

Mulla Sadra’s Theory of Substantial Motion[1]

Mohammad Javad Rezaei* Mahdi Dasht Bozorgi**  One of the most important philosophical theories of Mulla Sadra is substantial motion, which has greatly influenced other philosophical discussions. In this article, first we refer to the historical background of the theory before Mulla Sadra, namely in Peripatetic Philosophy, and then deal with Mulla Sadra’s innovations, such as ...

THE WEAK-TYPE (1, 1) OF FOURIER INTEGRAL OPERATORS OF ORDER −(n − 1)/2

Let T be a Fourier integral operator on R n of order −(n − 1)/2. In [4] it was shown (among other things) that T maps the Hardy space H 1 to L 1. In this note we show that T is also of weak-type (1, 1). The main ideas are a decomposition of T into non-degenerate and degenerate components, and a factorization of the non-degenerate portion.