Marcin Bownik

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The Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a(More)
Let A 1 and A 2 be expansive dilations, respectively, on R n and R m. Let A ≡ (A 1 , A 2) and A p (A) be the class of product Muckenhoupt weights on R n × R m for p ∈ (1, ∞]. When p ∈ (1, ∞) and w ∈ A p (A), the authors characterize the weighted Lebesgue space L p w (R n × R m) via the anisotropic Lusin-area function associated with A. When p ∈ (0, 1], w ∈(More)
Let S be a shift-invariant subspace of L 2 (R n) defined by N generators and suppose that its length L, the minimal number of generators of S, is smaller than N. Then we show that at least one reduced family of generators can always be obtained by a linear combination of the original generators, without using translations. In fact, we prove that almost(More)
For weights in the matricial Muckenhoupt classes we investigate a number of properties analogous to properties which hold in the scalar Muckenhoupt classes. In contrast to the scalar case we exhibit for each p, 1 < p < 1, a matrix weight W 2 A p;q n S p 0 <p A p 0 ;q 0. We also give a necessary and suucient condition on W in A p;q , a \reverse inverse(More)
In this article, the authors study weighted anisotropic Besov and Triebel-Lizorkin spaces associated with expansive dilations and A ∞ weights. The authors show that elements of these spaces are locally integrable when the smoothness parameter α is positive. The authors also characterize these spaces for small values of α in terms of a mean square function(More)