Abstract
We investigate the regularity of the set of all products \(f\cdot g\) for \(f\) and \(g\) belonging to certain Nikol’skii–Besov spaces. The special situation we are interested in has been left open in earlier contributions. It represents a limiting situation. We list a number of positive and negative results, both in the inhomogeneous and in the homogeneous situation.
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 312, pp. 170–187 https://doi.org/10.4213/tm4137.
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Sickel, W. On a Limiting Case for Pointwise Multiplication in Nikol’skii–Besov Spaces. Proc. Steklov Inst. Math. 312, 162–178 (2021). https://doi.org/10.1134/S0081543821010090
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DOI: https://doi.org/10.1134/S0081543821010090