We prove theorems on boundedness of operators weak type $(\varphi_0, \psi_0, \varphi_1, \psi_1)$ from Lorentz space $\Lambda_{\varphi,a}(\mathbb{R}^n)$ to $\Lambda_{\varphi,b}(\mathbb{R}^n)$ in “limit” cases, when one functions $\varphi(t) / \varphi_0(t)$, \varphi_1(t)$ slowly changes at zero and infinity.

Abstract The Jánossy density for a determinantal point process is the probability that an interval $I$ contains exactly $p$ points except those at $k$ designated loci. associated with integrable kernel $\mathbf{K}\doteq (\varphi(x)\psi(y)-\psi(x)\varphi(y))/(x-y)$ shown to be expressed as Fredholm determinant $\mathrm{Det}(\mathbb{I}-\tilde{\mathbf{K}}|_I)$ of transformed $\tilde{\mathbf{K}}\do...

We study the enumeration of Hamiltonian cycles on the thin grid cylinder graph Cm × Pn+1. We distinguish two types of Hamiltonian cycles depending on their contractibility (as Jordan curves) and denote their numbers h m (n) and hm(n). For fixedm, both of them satisfy linear homogeneous recurrence relations with constant coefficients. We derive their generating functions and other related result...

The pervasiveness of research agreements between pharmaceutical and biotechnology companies is puzzling, since it is hard to contract on the exact nature of the research activities. A major concern of financing companies is that the R&D firms use their funding to subsidize other projects or substitute one project for another. We develop a model based on the property-rights theory of the firm th...

Let $$\Omega \subset {\mathbb {C}}^n$$ be a smooth bounded pseudoconvex domain and $$A^2 (\Omega )$$ denote its Bergman space. $$P:L^2(\Omega )\longrightarrow A^2(\Omega the projection. For measurable $$\varphi :\Omega \longrightarrow \Omega $$ , projected composition operator is defined by $$(K_\varphi f)(z) = P(f \circ \varphi )(z), z \in f\in A^2 ).$$ In 1994, Rochberg studied boundedness of...

We provide a boundedness criterion for the integral operator $$S_{\varphi }$$ on fractional Fock–Sobolev space $$F^{s,2}({{\mathbb {C}}}^n)$$ , $$s\ge 0$$ where (introduced by Zhu [18]) is given $$\begin{aligned} S_{\varphi }F(z):= \int _{{\mathbb {C}}^n} F(w) e^{z \cdot \bar{w}} \varphi (z- \bar{w}) d\lambda (w) \end{aligned}$$ with $$\varphi $$ in Fock $$F^2({{\mathbb {C}}^n})$$ and $$d\lambd...