Marcin Preisner

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math.FA2024

Harmonic functions for Bessel operators

Michał Dymowski, Marcin Preisner, Adam Sikora

We verify the continuity of the Riesz transform from the operator related Hardy space to $L^{1}$ - Lebesgue space of integrable functions. For the standard Euclidean Laplace operator…

math.FA2018

Local atomic decompositions for multidimensional Hardy spaces

Edyta Kania, Paweł Plewa, Marcin Preisner

We consider a nonnegative self-adjoint operator $L$ on $L^{2} (X)$ , where $X \subseteq R^{d}$ . Under certain assumptions, we prove atomic characterizations of the Hardy space $$…

math.FA2018

Sharp multiplier theorem for multidimensional Bessel operators

Edyta Kania, Marcin Preisner

Consider the multidimensional Bessel operator $B f (x) = - j = 1 \sum N (\partial_{j}^{2} f (x) + \frac{α _{j}}{x _{j}} \partial_{j} f (x)), x \in (0, \infty)^{N} .$ Let $d = \sum_{j=…