The first chapters of this book deal with Haar bases, Faber bases and some spline bases for
function spaces in Euclidean $ n $-space and $ n $-cubes. These are used in the …

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Until now, no book has systematically presented the recently developed concept of
envelopes in function spaces. Envelopes are relatively simple tools for the study of classical …

In this article, we establish a characterization of the set M (B p,∞ 0, b (R n)) of all pointwise
multipliers of Besov spaces B p,∞ 0, b (R n) with only logarithmic smoothness b∈ R in the …

We study continuity envelopes in spaces of generalised smoothness Bpq (s, Ψ) and Fpq (s,
Ψ) and give some new characterisations for spaces Bpq (s, Ψ). The results are applied to …

In this paper we obtain a wavelet representation in (inhomogeneous) Besov spaces of
generalized smoothness via interpolation techniques. As consequence, we show that …

In this paper we present a comprehensive treatment of function spaces with logarithmic
smoothness (Besov, Sobolev, Triebel-Lizorkin). We establish the following results: Sharp …

In this article, the authors first establish the pointwise characterizations of Besov and Triebel—
Lizorkin spaces with generalized smoothness on ℝ n via the Hajłasz gradient sequences …

In this article, the authors study the Lebesgue point of functions from Hajłasz–Sobolev,
Besov, and Triebel–Lizorkin spaces with generalized smoothness on doubling metric …

We prove a lower bound estimate for capacities in Hajłasz–Besov, Hajłasz–Triebel–Lizorkin
and Hajłasz–Sobolev spaces with generalized smoothness defined on metric spaces in …