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Multiplication and factorization of functions in Sobolev spaces and in \(C_ p^ \alpha\) spaces on general domains. (English) Zbl 0851.46022

A class of function spaces, the definition of which involves a modification of one due to deVore and Sharpley (1984), is introduced. These function spaces include functions which are not locally integrable, and hence not distributions. The mapping properties of the operation of multiplying two functions from these spaces is examined, as is the associated problem of factoring a given function into such a product.
Reviewer: J.F.Toland (Bath)

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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