Supplement to multiplier theorems

Stability theorems for semi{groups via Multiplier theorems

0 Endpoint Multiplier Theorems of Marcinkiewicz Type

We establish sharp (H 1 , L 1,q) and local (L log r L, L 1,q) mapping properties for rough one-dimensional multipliers. In particular, we show that the multipliers in the Marcinkiewicz multiplier theorem map H 1 to L 1,∞ and L log 1/2 L to L 1,∞ , and that these estimates are sharp.

Central Multiplier Theorems for Compact Lie Groups

The purpose of this note is to describe how central multiplier theorems for compact Lie groups can be reduced to corresponding results on a maximal torus. We shall show that every multiplier theorem for multiple Fourier series gives rise to a corresponding theorem for such groups and, also, for expansions in terms of special functions. We use the notation and terminology of N. J. Weiss [4]. Let...

Transplantation and Multiplier Theorems for Fourier-bessel Expansions

Proved are weighted transplantation inequalities for Fourier-Bessel expansions. These extend known results on this subject by considering the largest possible range of parameters, allowing more weights and admitting a shift. The results are then used to produce a fairly general multiplier theorem with power weights for considered expansions. Also fractional integral results and conjugate functi...

Problems and Theorems in the Theory of Multiplier Sequences

The purpose of this paper is (1) to highlight some recent and heretofore unpublished results in the theory of multiplier sequences and (2) to survey some open problems in this area of research. For the sake of clarity of exposition, we have grouped the problems in three subsections, although several of the problems are interrelated. For the reader’s convenience, we have included the pertinent d...