Related papers: Operator-valued Triebel-Lizorkin spaces
In this paper we investigate the reproducing kernel Hilbert space where the polylogarithm appears as kernel functions. This investigation begins with the properties of functions in this space, and here a connection to the classical Hardy…
Let $\lambda>0$, $p\in((2\lz+1)/(2\lz+2), 1]$, and $\triangle_\lambda\equiv-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ be the Bessel operator. In this paper, the authors establish the characterizations of atomic Hardy spaces $H^p((0,…
We study the pointwise multiplier property of the characteristic function of the half-space on weighted mixed-norm anisotropic vector-valued function spaces of Bessel potential and Triebel-Lizorkin type.
In this paper, Mikhlin and Marcinkiewicz--Lizorkin type operator-valued multiplier theorems in weighted Lebesgue-Bochner spaces are studied. By using this results embedding theorems in Sobolev-Lions type spaces is obtained. Moreover,…
We introduce a new class of operators, called Berezin sectorial operators, which generalizes classical sectorial operators. We provide examples on the Hardy-Hilbert space showing that there exist operators that are Berezin sectorial but not…
We study the spaces of Besov and Triebel-Lizorkin type with variable smoothness and integrability as introduced recently by Almeida & H\"ast\"o and Diening, H\"ast\"o & Roudenko. Both scales cover many classical spaces with fixed exponents…
Through the study of novel variants of the classical Littlewood-Paley-Stein $g$-functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on $\mathbb{R}^d$ satisfying regularity hypotheses adapted to…
We develop local elliptic regularity for operators having coefficients in a range of Sobolev-type function spaces (Bessel potential, Sobolev-Slobodeckij, Triebel-Lizorkin, Besov) where the coefficients have a regularity structure typical of…
Let $p\in(1,\infty)$ and $q\in[1,\infty)$. In this article, the authors characterize the Triebel-Lizorkin space ${F}^\alpha_{p,q}(\mathbb{R}^n)$ with smoothness order $\alpha\in(0,2)$ via the Lusin-area function and the…
We introduce truncated Besov and Triebel--Lizorkin function spaces and investigate their main properties: embeddings, interpolation, duality, lifting, traces. These new scales allow us to improve several known results in functional analysis…
In this paper, by using the atomic decomposition theory of Hardy space and weak Hardy space, we discuss the boundedness of parameterized Littlewood-Paley operator with variable kernel on these spaces.
In this article, using growth functions we introduce generalized matrix-weighted Besov-Triebel-Lizorkin-type spaces with matrix $\mathcal{A}_{\infty}$ weights. We first characterize these spaces, respectively, in terms of the…
Weighted Triebel-Lizorkin and Besov spaces on the unit ball $B^d$ in $\Rd$ with weights $\W(x)= (1-|x|^2)^{\mu-1/2}$, $\mu \ge 0$, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized…
We address the function space theory associated with the Schroedinger operator H. The discussion is featured with the Poeschl-Teller potential in quantum physics. Using biorthogonal dyadic system, we introduce Besov spaces and…
We prove certain vector valued inequalities related to Littlewood-Paley theory on Euclidean spaces. They can be used in proving characterization of the Hardy spaces in terms of Littlewood-Paley operators by methods of real analysis.
The role of Liouville operators in the study of dynamical systems through the use of occupation measures have been an active area of research in control theory over the past decade. This manuscript investigates Liouville operators over the…
In this paper, by using the atomic decomposition theorem for weighted weak Hardy spaces, we will show the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and…
In this article, we study certain transcendental function spaces arising in potential theory within the framework of Orlicz spaces. Specifically, we generalize Bessel and Lizorkin-Triebel spaces to the nonstandard setting of Orlicz spaces.…
We introduce variable exponent versions of Morreyfied Triebel-Lizorkin spaces. To that end, we prove an important convolution inequality which is a replacement for the Hardy-Littlewood maximal inequality in the fully variable setting. Using…
We study three-dimensional partition functions constructed from the tetrahedral $L$-operator introduced and studied by Bazhanov-Sergeev and Kuniba-Maruyama-Okado. First, we explore the $q=0$ case, extending the authors' previous results and…