Let X be a ball quasi-Banach function space on $${{\mathbb {R}}}^n$$ and assume that the Hardy–Littlewood maximal operator satisfies Fefferman–Stein vector-valued inequality X, let $$q\in [1,\infty )$$ $$d\in (0,\infty . In this article, authors prove that, for any $$f\in {\mathcal {L}}_{X,q,0,d}({\mathbb {R}}^n)$$ (the Campanato-type associated with X), Littlewood–Paley g-function g(f) is eith...

The space of metric measure spaces (complete separable metric spaces with a probability measure) is becoming more and more important as state space for stochastic processes. Of particular interest is the subspace of (continuum) metric measure trees. Greven, Pfaffelhuber and Winter introduced the Gromov-Prohorov metric dGP on the space of metric measure spaces and showed that it induces the Grom...

We extend previous results on the spectral distribution of discretization matrices arising from Bspline Isogeometric Analysis (IgA) approximations of a general d-dimensional second-order elliptic Partial Differential Equation (PDE) with variable coefficients. First, we provide the spectral symbol of the Galerkin B-spline IgA stiffness matrices, assuming only that the PDE coefficients belong to ...

2 This is shown for C the unit circle by an example of Lusin and Privalov in Priwalow, I. I., Randeigenschaften analytischer Funktionen (Berlin, 1956), pp. 229-230; and for general C by Bagemihl, F., and W. Seidel, "Regular functions with prescribed measurable boundary values almost everywhere," these PROCEEDINGS, 41, 740-743 (1955), Theorem 2. 8 See Golusin, G. M., Geometrische Funktionentheor...