Contractive inequalities for mixed norm spaces and the Beta function
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DOI: 10.1016/j.jmaa.2021.125938
Abstract: For a wide range of pairs of mixed norm spaces such that one space is contained in another, we characterize all cases when contractive norm inequalities hold. In particular, this yields such results for many… read more here.
Keywords: beta function; mixed norm; spaces beta; norm spaces ... See more keywords
Embeddings of harmonic mixed norm spaces on smoothly bounded domains in ℝn
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DOI: 10.1515/math-2019-0108
Abstract: Abstract The main result of this paper is the embedding Bβs,r(Ω)↪Bβ+(n−1)(1s−1s1)s1,r1(Ω), $$\begin{array}{} \displaystyle \mathcal{B}^{s,r}_\beta({\it\Omega})\hookrightarrow \mathcal{B}^{s_1,r_1}_{\beta+(n-1)\big(\frac 1s-\frac 1{s_1}\big)}({\it\Omega}), \end{array}$$ 0 < r ≤ r1 ≤ ∞, 0 < s ≤ s1 ≤ ∞, β > –1,… read more here.
Keywords: smoothly bounded; embeddings harmonic; mixed norm; spaces smoothly ... See more keywords
Wavelets in weighted norm spaces
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DOI: 10.2748/tmj/1546570826
Abstract: We give a complete characterization of the classes of weight functions for which the Haar wavelet system for $m$-dilations, $m= 2,3,\ldots$ is an unconditional basis in $L^p(\mathbb{R},w)$. Particulary it follows that higher rank Haar wavelets… read more here.
Keywords: norm spaces; weighted norm; wavelets weighted;