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Structure of the quotient modules in $hh$ is very complicated. A good understanding of some special examples will shed light on the general picture. This paper studies the so-call $N_{p}$-type quotient modules, namely, quotient modules of the form $hhominus [z-p]$, where $p (w)$ is a function in the classical Hardy space $H^2(G)$ and $[z-p]$ is the submodule generated by $z-p (w)$. This type of quotient modules serve as good examples in many studies. A notable feature of the $N_{p}$-type quotient module is its close connections with some classical single variable operator theories.
In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on $L^p$-spaces. First, we prove analogues of k
The paper studies the sampling discretization problem for integral norms on subspaces of $L^p(mu)$. Several close to optimal results are obtained on subspaces for which certain Nikolskii-type inequality is valid. The problem of norms discretization i
We study submodules of analytic Hilbert modules defined over certain algebraic varieties in bounded symmetric domains, the so-called Jordan-Kepler varieties $V_ell$ of arbitrary rank $ell.$ For $ell>1$ the singular set of $V_ell$ is not a complete in
We investigate the correlation between integrated proton-neutron interactions obtained by using the up-to-date experimental data of binding energies and the $N_{rm p} N_{rm n}$, the product of valence proton number and valence neutron number with res
We obtain sharp ranges of $L^p$-boundedness for domains in a wide class of Reinhardt domains representable as sub-level sets of monomials, by expressing them as quotients of simpler domains. We prove a general transformation law relating $L^p$-bounde