On rearrangements of the Haar system in the space BMO

Abstract

The effects of fluorine on superconducting properties and microstructures of top-seeded melt grown YBa 2 Cu 3 O 7−δ bulks have been investigated through BaF 2 additions (up to 1 wt% BaF 2 ). DTA measurements show that the decomposition temperature is lowered when the content of BaF 2 is increased (1003 • C for the sample doped with 1 wt% BaF 2 ). The microstructures of the doped samples are similar to those observed in fluorine-free samples. In particular, a negligible effect is observed on the size of the Y211 particles. In the same way, the superconducting properties do not change with the additions of BaF 2 . DTA measurements of heavily doped compositions (up to 10 wt% BaF 2 ) show that the decomposition temperature is lowered down to 969 • C for an addition of 5 wt% BaF 2 . This makes BaF 2 additions promising to replace silver additions in welding processes.

The Haar wavelet characterization of weighted Herz spaces and greediness of the Haar wavelet basis

“…The proof we give here is essentially the same as in [3,Section 5.3]. We see that the sequence {ϕ 0,k , ψ ε j,k : ε ∈ E, j ∈ N 0 , k ∈ Z n } forms an unconditional basis for L p (w) by Theorem 19. Thus for all f ∈ L p (w) we can write…”

“…Indeed, starting from this paper, many authors still investigate the properties of the Haar wavelet (see [4,7,[16][17][18][19]). This paper is oriented to the characterization in terms of the Haar wavelets.…”