First order -variations and Besov spaces
Copyright policy )First order -variations and Besov spaces
For a real function \(f\) on \([0,\,1]\) and \(01/p, \,1\leq p, q\leq \infty\). The usual norm of the Besov spaces \(\mathcal{B}_{p,q}^{s}([0,1])\) is equivalent to the norm defined by \[ \|f\|=\max \Big\{|f(0)|, \Big(\sum_{j\geq 0}2^{jq(s-1/p)}\{V_{j}^{p}(f)\}^{q/p}\Big)^{1/q}\Big\}. \] (2) Let \(f: [0,\,1] \rightarrow \mathbb{R}\) be a Borel function and \(0
Distributions, generalized functions, distribution spaces, Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable, Continuous time stochastic processes, Besov spaces, Gaussian processes, Sample path properties, Nontrigonometric harmonic analysis involving wavelets and other special systems, First order dyadic \(p\)-variation
Distributions, generalized functions, distribution spaces, Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable, Continuous time stochastic processes, Besov spaces, Gaussian processes, Sample path properties, Nontrigonometric harmonic analysis involving wavelets and other special systems, First order dyadic \(p\)-variation
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