9. Juli 2025

Tillmann Kleiner (FU Berlin)

On Convolution on Amalgam Spaces of Distributions

Classical amalgam spaces are Banach spaces of measurable functions that are composed of a global component, determining the growth behaviour of the functions at infinity, and a local component, that determines the local regularity of the functions. The archetypical amalgam space W(L^p, L^q) has L^p as global component and L^q as local component. These spaces are convenient for the study of convolution and multiplication operators, because their effects on global and local properties of functions can be considered seperately.

This talk gives an introduction to amalgam spaces of distributions and some properties of convolution on these spaces. These spaces were introduced and studied recently for general global components and have the space of distributions itself as local component. The classical distribution spaces introduced by Laurent Schwartz, such as distributions with L^p-like global behaviour, could be characterized as amalgam spaces of distributions. Combining this with discrete global components for amalgam spaces allowed to simplify and settle the characterization of continuity of convolution between power weighted spaces of distributions with L^p-like global behaviour.

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