On inclusion relations of weighted -type spaces defined in terms of weight function matrices
arXiv:2510.05469 · doi:10.1016/j.jmaa.2026.130705
Abstract
We introduce new weighted -type spaces defined in terms of weight function matrices and characterize the inclusion relations in terms of the defining matrices. Moreover, we provide a detailed study concerning the coincidence with the common (non-weighted) -spaces, the (non-)triviality of such weighted spaces and investigate their translation invariance. The obtained results are then applied to particular weight function matrices which are expressed in terms of one single weight function and a positive real parameter. Also variations of this new weighted setting are discussed; more precisely weighted Banach (sub-)spaces of and when weighting the Fourier image of appropriate Banach spaces of functions. The general framework allows to describe the known ultradifferentiable weight function setting by Beurling-Björck which is more original than the approach presented by Braun, Meise and Taylor. When applying the characterization of the inclusion relations to Beurling-Björck-type spaces we are able to emphasize the difference between both ultradifferentiable weight function settings: We construct a technical (counter-)example which is a weight in the sense of Beurling Björck but violates the standard and crucial convexity condition needed in the Braun-Meise-Taylor setting.
47 pages; some typos have been corrected; this version is published in J. Math. Anal. Appl
References in corpus (8)
- On generalized definitions of ultradifferentiable classes
- On the regularization of sequences and associated weight functions
- On inclusion relations between weighted spaces of entire functions
- On strong growth conditions for weighted spaces of entire functions
- The Borel map in the mixed Beurling setting
- On optimal solutions of the Borel problem in the Roumieu case
- Kernel theorems for Beurling-Björck type spaces
- On the inclusion relations between Gelfand-Shilov spaces