Related papers: A subordination Principle. Applications

Introduced by Coifman, Meyer, and Stein, the tent spaces have seen wide applications in Harmonic Analysis. Their analytic cousins have seen some applications involving the derivatives of Hardy space functions. Moreover, the tent spaces have…

In this article, we determine conditions on the parameters of a generalized convolution operator such that it belongs to the Hardy space and to the space of bounded analytic functions. Results obtained are new and their usefulness is…

The homogeneous causal action principle on a compact domain of momentum space is introduced. The connection to causal fermion systems is worked out. Existence and compactness results are reviewed. The Euler-Lagrange equations are derived…

A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…

Let P be a linear, second order, elliptic operator satisfying a Hardy inequality with potential W (i.e. $P-W\geq0$) and best constant $\alpha$. We give conditions so that the spectrum of $W^{-1}P$ is $[\alpha,\infty)$. We apply this to…

The main result (roughly) is that if (H_i) converges weakly to H and if also f(H_i) converges weakly to f(H), for a single strictly convex continuous function f, then (H_i) must converge strongly to H. One application is that if f(pr(H)) =…

In this work, we prove that if S is a dual bounded sequence in the unit ball B of C^n for the Hardy class H^p(B), then S is H^s(B) interpolating with the linear extension property.

When a function belonging to a fractional-order Sobolev space is supported in a proper subset of the Lipschitz domain on which the Sobolev space is defined, how is its Sobolev norm as a function on the smaller set compared to its norm on…

In this paper we propose a counterexample to the validity of the Comparison Principle and of the Sub and Supersolution Method for nonlocal problems like the stationary Kirchhoff Equation. This counterexample shows that in general smooth…

We realize the Belinschi-Nica semigroup of homomorphisms as a free multiplicative subordination. This realization allows to define more general semigroups of homomorphisms with respect to free multiplicative convolution. For these…

A classical observation of Riesz says that truncations of a general $\sum_{n=0}^\infty a_n z^n$ in the Hardy space $H^1$ do not converge in $H^1$. A substitute positive result is proved: these partial sums always converge in the Bergman…

A theorem that is of aid in computing the domain of the adjoint operator is provided. It may serve e.g. as a criterion for selfadjointness of a symmetric operator, for normality of a formally normal operator or for $H$--selfadjointness of…

For a wide class of domains $G\subset\mathbb C^d$ including balls and polydisks we prove the density of their canonical image in the spectrum of $H^\infty(G)$. This Corona Theorem is proved first in its abstract version for certain uniform…

In this article we consider linear operators satisfying a generalized commutation relation of a type of the Heisenberg-Lie algebra. It is proven that a generalized inequality of the Hardy's uncertainty principle lemma follows. Its…

The object of this paper is to prove a version of the Beurling-Helson-Lowdenslager invariant subspace theorem for operators on certain Banach spaces of functions on a multiply connected domain in the complex plane. The norms for these…

The validity of Korn's first inequality in the fractional setting in bounded domains has been open. We resolve this problem by proving that in fact Korn's first inequality holds in the case $ps>1$ for fractional $W^{s,p}_0(\Omega)$ Sobolev…

In this paper, we consider a large class of subordinate Brownian motions $X$ via subordinators with Laplace exponents which are complete Bernstein functions satisfying some mild scaling conditions at zero and at infinity. We first discuss…

In this paper first we define generalized Carleson mea- sure. Then we consider a special case of it, named conditional Carleson measure on the Bergman spaces. After that we give a characterization of conditional Carleson measures on Bergman…

We consider the so-called Dickman subordinator, whose Levy measure has density 1/x restricted to the interval (0,1). The marginal density of this process, known as the Dickman function, appears in many areas of mathematics, from number…

Let ${H^p}\left( \mathbb{D} \right)$ be the Hardy space of all holomorphic functions on the unit disk $\mathbb{D}$ with exponent $p>0$. If $D\ne \mathbb{C}$ is a simply connected domain and $f$ is the Riemann mapping from $\mathbb{D}$ onto…