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A gradient-projective basis of compactly supported wavelets in dimension n > 1

Guy Battle (2013)

Open Mathematics

A given set W = W X of n-variable class C 1 functions is a gradient-projective basis if for every tempered distribution f whose gradient is square-integrable, the sum ∑ χ ( ∫ ℝ n ∇ f · ∇ W χ * ) W χ converges to f with respect to the norm ∇ ( · ) L 2 ( ℝ n ) . The set is not necessarily an orthonormal set; the orthonormal expansion formula is just an element of the convex set of valid expansions of the given function f over W. We construct a gradient-projective basis W = W x of compactly supported class C 2−ɛ functions on ℝn such that [...]...

A note on multilinear Muckenhoupt classes for multiple weights

Songqing Chen, Huoxiong Wu, Qingying Xue (2014)

Studia Mathematica

This paper is devoted to investigating the properties of multilinear A P ⃗ conditions and A ( P ⃗ , q ) conditions, which are suitable for the study of multilinear operators on Lebesgue spaces. Some monotonicity properties of A P ⃗ and A ( P ⃗ , q ) classes with respect to P⃗ and q are given, although these classes are not in general monotone with respect to the natural partial order. Equivalent characterizations of multilinear A ( P ⃗ , q ) classes in terms of the linear A p classes are established. These results essentially improve and extend...

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