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papers

Publications (16)

math.FA2023

Hardy spaces meet harmonic weights revisited

Marcin Preisner, Adam Sikora

We investigate Hardy spaces $H_{L}^{1} (X)$ corresponding to self-adjoint operators $L$ . Our main aim is to obtain a description of $H_{L}^{1} (X)$ in terms of atomic decompositions similar…

math.FA2017

Hardy spaces for semigroups with Gaussian bounds

Jacek DziubaÅski, Marcin Preisner

Let T_t=e^{-tL} be a semigroup of self-adjoint linear operators acting on L^2(X,mu), where (X,d mu) is a space of homogeneous type. We assume that T_t has an integral kernel T_t(x,…

math.FA2020

Sharp multiplier theorem for multidimensional Bessel operators

Edyta Kania, Marcin Preisner

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

math.FA2020

Local atomic decompositions for multidimensional Hardy spaces

Edyta Kania, PaweÅ 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.FA2024

Harmonic functions for Bessel operators

MichaÅ 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.FA2010

Remarks on spectral multiplier theorems on Hardy spaces associated with semigroups of operators

Jacek DziubaÅski, Marcin Preisner

Let L be a non-negative, self-adjoint operator on L^2(Î©), where (Î©, d Î¼) is a space of homogeneous type. Assume that the semigroup {T_t}_{t>0} generated by -L satisfies Gaussian…

math.FA2014

Atomic decompositions for Hardy spaces related to SchrÃ¶dinger operators

Marcin Preisner

Let L_U = -Delta+U be a SchrÃ¶dinger operator on R^d, where U\in L^1_{loc}(R^d) is a non-negative potential and d\geq 3. The Hardy space H^1(L_U) is defined in terms of the maximal…

math.FA2011

Riesz transform characterization of H^1 spaces associated with certain Laguerre expansions

Marcin Preisner

For alpha>0 we consider the system l_k^{(alpha-1)/2}(x) of the Laguerre functions which are eigenfunctions of the differential operator Lf =-\frac{d^2}{dx^2}f-\frac{alpha}{x}\frac{…

math.FA2010

On Riesz transforms characterization of H^1 spaces associated with some SchrÃ¶dinger operators

Jacek DziubaÅski, Marcin Preisner

Let Lf(x)=-Îf(x) + V(x)f(x), V\geq 0, V\in L^1_{loc}(R^d), be a non-negative self-adjoint SchrÃ¶dinger operator on R^d. We say that an L^1-function f belongs to the Hardy space H^…

math.FA2021

Hardy spaces meet harmonic weights

Marcin Preisner, Adam Sikora, Lixin Yan

We investigate the Hardy space $H_{L}^{1}$ associated with a self-adjoint operator $L$ defined in a general setting in [S. Hofmann, et. al., Hardy spaces associated to non-negative sel…

math-ph2018

Kinetic energy represented in terms of moments of vorticity and applications

Tomasz CieÅlak, Krzysztof Oleszkiewicz, Marcin Preisner +1

We study 2d vortex sheets with unbounded support. First we show a version of the Biot- Savart law related to a class of objects including such vortex sheets. Next, we give a formul…

math.FA2009

Riesz transform characterization of Hardy spaces associated with SchrÃ¶dinger operators with compactly supported potentials

Jacek DziubaÅski, Marcin Preisner

Let L=-Î+V be a SchrÃ¶dinger operator on R^d, d\geq 3. We assume that V is a nonnegative, compactly supported potential that belongs to L^p(R^d), for some p>d/2. Let K_t be the se…

math.FA2011

Hardy spaces related to SchrÃ¶dinger operators with potentials which are sums of L^p-functions

Jacek DziubaÅski, Marcin Preisner

We investigate the Hardy space H^1_L associated to the SchrÃ¶dinger operator L=-Î+V on R^n, where V=\sum_{j=1}^d V_j. We assume that each V_j depends on variables from a linear su…

math.FA2021

Riesz transform characterizations for multidimensional Hardy spaces

Edyta Kania-Strojec, Marcin Preisner

We study Hardy space $H_{L}^{1} (X)$ related to a self-adjoint operator $L$ defined on Euclidean domain $X \subseteq R^{d}$ . Under certain assumptions on the heat semigroup $\exp…

math.FA2011

Multivariate HÃ¶rmander-type multiplier theorem for the Hankel transform

Jacek DziubaÅski, Marcin Preisner, BÅaÅ¼ej WrÃ³bel

Let H(f)(x)=\int_{(0,infty)^d} f(v) E_{x}(v) dÎ½(v), be the multivariable Hankel transform, where E_{x}(v)=\prod_{k=1}^d (x_k v_k)^{-a_k+1/2} J_{a_k-1/2}(x_k v_k), dÎ½(v)=v^a dv, a…

math.CA2017

Hardy spaces for Bessel-SchrÃ¶dinger operators

Edyta Kania, Marcin Preisner

Consider the Bessel operator with a potential on L^2((0,infty), x^a dx), namely Lf(x) = -f"(x) - a/x f'(x) + V(x)f(x). We assume that a>0 and V\in L^1_{loc}((0,infty), x^a dx) is a…