# Edyta Kania-StrojecUniversity of Wroclaw | WROC · Instytut Matematyczny

Edyta Kania-Strojec

Master of Science

## About

4

Publications

175

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9

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Introduction

## Publications

Publications (4)

Consider the multidimensional Bessel operator Bf(x)=-∑j=1N(∂j2f(x)+αjxj∂jf(x)),x∈(0,∞)N.Let d=∑j=1Nmax(1,αj+1) be the dimension of the space (0 , ∞) N equipped with the measure x1α1…xNαNdx1…dxN. In the general case α 1 , … , α N > - 1 we prove multiplier theorems for spectral multipliers m(B) on L ¹,∞ and the Hardy space H ¹ . We assume that m sati...

We consider a nonnegative self-adjoint operator $L$ on $L^2(X)$, where $X\subseteq \mathbb{R}^d$. Under certain assumptions, we prove atomic characterizations of the Hardy space $$H^1(L) = \left\{f\in L^1(X) \ : \ \left\|\sup_{t>0} \left|\exp(-tL)f \right| \right\|_{L^1(X)}<\infty\right\}.$$ We state simple conditions, such that $H^1(L)$ is charact...

Consider the multidimensional Bessel operator $$B f(x) = -\sum_{j=1}^N \left(\partial_j^2 f(x) +\frac{\alpha_j}{x_j} \partial_j f(x)\right), \quad x\in(0,\infty)^N. $$ Let $d = \sum_{j=1}^N \max(1,\alpha_j+1)$ be the homogeneous dimension of the space $(0,\infty)^N$ equipped with the measure $x_1^{\alpha_1}... x_N^{\alpha_N} dx_1...dx_N$. In the ge...

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 non-negative function. By definition, a function f\in L^1((0,infty), x^a dx) belongs to the Hardy space H^1(L) if sup_{t>0} |e^{-tL} f| \in L^1((0,infty), x^a dx). Unde...