Related papers: Wolff's Ideal Theorem on Qp Spaces

We study linear extremal problems in the Bergman space $A^p$ of the unit disc for $p$ an even integer. Given a functional on the dual space of $A^p$ with representing kernel $k \in A^q$, where $1/p + 1/q = 1$, we show that if the Taylor…

Let $\mathscr{C}_n=\{-1,1\}^n$ be the discrete hypercube equipped with the uniform probability measure $\sigma_n$. We prove that if $(E,\|\cdot\|_E)$ is a Banach space of finite cotype and $p\in[1,\infty)$, then every function…

The classical Grauert and Ramspott theorems constitute the foundation of the Oka principle on Stein spaces. In this paper we establish analogous results on the maximal ideal space $M(H^\infty)$ of the Banach algebra $H^\infty$ of bounded…

We study $H^p$ spaces of Dirichlet series, called $\mathcal{H}^p$, for the range $0<p< \infty$. We begin by showing that two natural ways to define $\mathcal{H}^p$ coincide. We then proceed to study some linear space properties of…

We study membership of rational inner functions in Dirichlet-type spaces in polydisks. In particular, we prove a theorem relating such inclusions to $H^p$ integrability of partial derivatives of a RIF, and as a corollary we prove that all…

It is well known that the only proper non-trivial norm-closed ideal in the algebra L(X) for X=\ell_p (1 \le p < \infty) or X=c_0 is the ideal of compact operators. The next natural question is to describe all closed ideals of…

We study $p$-harmonic functions, $ 1 < p\neq 2 < \infty$, in $ \mathbb{R}^{2}_+ = \{ z = x + i y : y > 0, - \infty < x < \infty \} $ and $B( 0, 1 ) = \{ z : |z| < 1 \}$. We first show for fixed $ p$, $1 < p\neq 2 < \infty$, and for all…

We show that there are $2^{2^{\aleph_0}}$ different closed ideals in the Banach algebra $L(L_p(0,1))$, $1<p\not= 2<\infty$. This solves a problem in A. Pietsch's 1978 book "Operator Ideals". The proof is quite different from other methods…

The class $M^p$ $(1<p<\infty)$ consists of all holomorphic functions $f$ on the open unit disk $\Bbb D$ for which $$ \int_0^{2\pi}\left(\log^+Mf(\theta)\right)^p\,\frac{d\theta}{2\pi}<\infty, $$ where $Mf(\theta)=\sup_{0\leqslant…

Let $\mathscr{H}^\infty$ be the set of all Dirichlet series $f=\sum\limits_{n=1}^\infty \frac{a_n}{n^s}$ (where $a_n\in \mathbb{C}$ for each $n$) that converge at each $s\in {\mathbb{C}}_+$, such that $\|f\|_{\infty}:=\sup_{s\in…

We study estimates for Hardy space norms of analytic projections. We first find a sufficient condition for the Bergman projection of a function in the unit disc to belong to the Hardy space $H^p$ for $1 < p < \infty$. We apply the result to…

We study absolute summability of inclusions of r.i. function spaces. It appears that such properties are closely related, or even determined by absolute summability of inclusions of subspaces spanned by the Rademacher system in respective…

For $p\in [1,\infty)$ we study representations of a locally compact group $G$ on $L^p$-spaces and $QSL^p$-spaces. The universal completions $F^p(G)$ and $F^p_{\mathrm{QS}}(G)$ of $L^1(G)$ with respect to these classes of representations…

In this paper we give an explicit description of the universal unitary completion of certain locally Q_p-analytic representations of GL_2(F), where F is a finite extension of Q_p (this generalizes some results of Berger-Breuil for F=Q_p).…

For $1<p\le \infty$, we show the existence of a Banach space which is both injectively and surjectively universal for the class of all separable Banach spaces with an equivalent $p$-asymptotically uniformly smooth norm. We prove that this…

For any $p\in[1,\infty)$, we prove that the set of simple functions taking at most $k$ different values is proximinal in B\"ochner spaces $L^p(X)$ whenever $X$ is a dual Banach space with $w^*$-sequentially compact unit ball. With…

We develop an existence, regularity and potential theory for nonlinear integrodifferential equations involving measure data. The nonlocal elliptic operators considered are possibly degenerate and cover the case of the fractional…

We consider the spaces $A_p(\mathbb T)$ of functions $f$ on the circle $\mathbb T$ such that the sequence of Fourier coefficients $\fu{\f}=\{\fu{\f}(k), ~k \in \mathbb Z\}$ belongs to $l^p, ~1\leq p<2$. The norm on $A_p(\mathbb T)$ is…

For $d = 2, 3, \ldots$ and $p \in [1, \infty),$ we define a class of representations $\rho$ of the Leavitt algebra $L_d$ on spaces of the form $L^p (X, \mu),$ which we call the spatial representations. We prove that for fixed $d$ and $p,$…

Let $\mu$ be a nonnegative Borel measure on the open unit disk $\mathbb{D}\subset\mathbb{C}$. This note shows how to decide that the M\"obius invariant space $\mathcal{Q}_p$, covering $\mathcal{BMOA}$ and $\mathcal{B}$, is boundedly (resp.,…