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- W4298389820 abstract "The question is addressed of when a Sobolev type space, built upon a general rearrangement-invariant norm, on an $n$-dimensional domain, is a Banach algebra under pointwise multiplication of functions. A sharp balance condition among the order of the Sobolev space, the strength of the norm, and the (ir)regularity of the domain is provided for the relevant Sobolev space to be a Banach algebra. The regularity of the domain is described in terms of its isoperimetric function. Related results on the boundedness of the multiplication operator into lower-order Sobolev type spaces are also established. The special cases of Orlicz-Sobolev and Lorentz-Sobolev spaces are discussed in detail. New results for classical Sobolev spaces on possibly irregular domains follow as well." @default.
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- W4298389820 date "2015-12-10" @default.
- W4298389820 modified "2023-09-28" @default.
- W4298389820 title "Banach algebras of weakly differentiable functions" @default.
- W4298389820 doi "https://doi.org/10.48550/arxiv.1512.03198" @default.
- W4298389820 hasPublicationYear "2015" @default.
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