An estimation of singular values of convolution operators

Singular Convolution Operators on the Heisenberg Group

1. Statement of results and outline of method. The purpose of this note is to announce results dealing with convolution operators on the Heisenberg group. As opposed to the well-known situation where the kernels are homogeneous and C°° away from the origin, the kernels we study are homogeneous but have singularities on a hyperplane. Convolution operators with such kernels arise in the study of ...

Inequalities for Strongly Singular Convolution Operators

Singular values of convex functions of matrices

‎Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $‎sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $‎sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$  are nonzero matrices and each $X_{i}$ is‎ ‎positive semidefinite‎. ‎It is shown that if $f$ is a nonnegative increasing ‎convex function on $left[ 0,infty right) $ satisfying $fleft( 0right)‎ ‎=0 $‎, ‎then  $$‎2s_{j}left( fleft( fra...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Strongly Singular Convolution Operators on the Heisenberg Group

We consider the L mapping properties of a model class of strongly singular integral operators on the Heisenberg group H; these are convolution operators on H whose kernels are too singular at the origin to be of Calderón-Zygmund type. This strong singularity is compensated for by introducing a suitably large oscillation. Our results are obtained by utilizing the group Fourier transform and unif...