17 citations · 41 across the 12 of their papers we have counts for
16 papers
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 - Lebesgue space of integrable functions. For the standard Euclidean Laplace operator…
Hardy spaces meet harmonic weights revisited
Marcin Preisner, Adam Sikora
We investigate Hardy spaces corresponding to self-adjoint operators . Our main aim is to obtain a description of in terms of atomic decompositions similar…
Riesz transform characterizations for multidimensional Hardy spaces
Edyta Kania-Strojec, Marcin Preisner
We study Hardy space related to a self-adjoint operator defined on Euclidean domain . Under certain assumptions on the heat semigroup $\exp…
Hardy spaces meet harmonic weights
Marcin Preisner, Adam Sikora, Lixin Yan
We investigate the Hardy space associated with a self-adjoint operator defined in a general setting in [S. Hofmann, et. al., Hardy spaces associated to non-negative sel…
Local atomic decompositions for multidimensional Hardy spaces
Edyta Kania, Paweł Plewa, Marcin Preisner
We consider a nonnegative self-adjoint operator on , where . Under certain assumptions, we prove atomic characterizations of the Hardy space $$…
Sharp multiplier theorem for multidimensional Bessel operators
Edyta Kania, Marcin Preisner
Consider the multidimensional Bessel operator Let $d = \sum_{j=…
Kinetic energy represented in terms of moments of vorticity and applications
Tomasz Cieślak, 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…
Hardy spaces for semigroups with Gaussian bounds
Jacek Dziubański, 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,…
Hardy spaces for Bessel-Schrödinger 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…
Atomic decompositions for Hardy spaces related to Schrödinger operators
Marcin Preisner
Let L_U = -Delta+U be a Schrödinger 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…
Hardy spaces for Fourier--Bessel expansions
J. Dziubański, M. Preisner, L. Roncal +1
We study Hardy spaces for Fourier--Bessel expansions associated with Bessel operators on and . We define Hardy spaces as the sets of $L^…
Multivariate Hörmander-type multiplier theorem for the Hankel transform
Jacek Dziubański, Marcin Preisner, Błażej Wróbel
Let H(f)(x)=\int_{(0,infty)^d} f(v) E_{x}(v) dν(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), dν(v)=v^a dv, a=(…
Hardy spaces related to Schrödinger operators with potentials which are sums of L^p-functions
Jacek Dziubański, Marcin Preisner
We investigate the Hardy space H^1_L associated to the Schrödinger operator L=-Δ+V on R^n, where V=\sum_{j=1}^d V_j. We assume that each V_j depends on variables from a linear subs…
On Riesz transforms characterization of H^1 spaces associated with some Schrödinger operators
Jacek Dziubański, Marcin Preisner
Let Lf(x)=-Δf(x) + V(x)f(x), V\geq 0, V\in L^1_{loc}(R^d), be a non-negative self-adjoint Schrödinger operator on R^d. We say that an L^1-function f belongs to the Hardy space H^1_…
Riesz transform characterization of Hardy spaces associated with Schrödinger operators with compactly supported potentials
Jacek Dziubański, Marcin Preisner
Let L=-Δ+V be a Schrödinger 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 semi…
Remarks on spectral multiplier theorems on Hardy spaces associated with semigroups of operators
Jacek Dziubański, Marcin Preisner
Let L be a non-negative, self-adjoint operator on L^2(Ω), where (Ω, d μ) is a space of homogeneous type. Assume that the semigroup {T_t}_{t>0} generated by -L satisfies Gaussian bo…