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About 2,039 papers for “weighted function spaces”

Weighted rearrangement-invariant function spaces

Filip Soudský · Digital Repository (National Repository of Grey Literature) · 2011

In this thesis we focus on generalized Gamma spaces GΓ(p, m, v) and classify some of their intrinsic properties. In an article called Relative Re- arrangement Methods for Estimating Dual Norm (for details see references), the authors attempted to characterize their associate norms but obtained only several one-sided estimates. Equipped with these, they further showed reflexivity of gener- alized Gamma spaces for p ≥ 2 and m > 1 under an additional restriction that the underlying measure space is of finite measure. However, the full characterization of the associate norm and of the reflexivity of such spaces for 2 > p > 1 remained an open problem. In this thesis we shall fill this gap. We extend the theory to a σ-finite measure space. We present a complete characterization of the associate norm, and we find necessary and sufficient conditions for the reflexivity of such spaces. 1

Cited by 0

Effective dimension for weighted function spaces

Art B. Owen · 2012

This paper introduces some notions of effective dimension for weighted function spaces. A space has low effective dimension if the smallest ball in it that contains a function of variance 1, has no functions with large values of certain ANOVA mean squares. For a Hilbert space defined by product weights we get explicit formulas describing effective dimension in terms of those weights. In particular, for a space with product weights it is possible to compute truncation and superposition dimensions directly from the weight sequence. For weights γj = γ1j −q with q> 1, and γj � 1, the result is a low superposition dimension though high truncation dimensions are possible. 1

Cited by 0

Weighted function spaces: convolutors, multipliers, and mollifiers

Lenny Neyt, Yoshihiro Sawano · ArXiv.org · 2025

We study smooth function spaces of Gelfand-Shilov type, with global behavior governed through a translation-invariant Banach function space and localized via a weight function system. We clarify the roles of the translation-invariant Banach function space, convolution, and pointwise multiplication in connection with the weight function system. Our primary goal is to characterize these function spaces-as well as the corresponding convolutor and multiplier spaces-through mollification. For this purpose, we introduce the moment-wise decomposition factorization property for pairs of compactly supported smooth functions, and establish complete characterizations in terms of mollifications with these windows.

Cited by 0Open access

Dynamics on weighted solid Banach function spaces

Stefan Ivković · ArXiv.org · 2025

The dynamics of weighted translation operators on Lebesgue spaces, Orlicz spaces, and in general on solid Banach function spaces have been studied in numerous papers. Recently, the dynamics of weighted translations on weighted Orlicz spaces have also been studied by Chen and others. The main idea of this paper is to obtain a generalization of these results to the case of general weighted solid Banach function spaces. More precisely, in this paper, we characterize disjoint topologically transitive and disjoint supercyclic weighted composition operators on weighted solid Banach function spaces. This approach has applications in the dynamics of weighted translations on weighted Morrey spaces.

Cited by 0Open access

Weighted function spaces and traces on fractals

Iwona Piotrowska · Common Library Network (Der Gemeinsame Bibliotheksverbund) · 2006

Das wesentliche Thema in der allgemeinen Theorie der Funktionenräume der vergangenen Jahrzehnte ist die Untersuchung der Zusammenhänge zwischen Funktionen-räumen, Fourieranalysis und Spektraltheorie von Differentialoperatoren und in letzter Zeit auch zur Fraktalen Geometie. Wir benutzen in unserer Arbeit sowohl fundamentale Ideen aus der Theorie der Funktionenräume als auch Methoden der Fraktalen Geometrie, um die Zusammenhänge zwischen Fraktalen und gewichteten Funktionenräumen vom Besov- und Triebel-Lizorkin-Typ, bezeichnet mit Bspq(Rn,w) bzw. Fsp(Rn,w), zu studieren. In der gesamten Arbeit werden wir Gewichtsfunk- tionen betrachten, welche zu einer Muckenhoupt Klasse Ap mit 1 < p < ∞ gehören. Die Klasse Ap von Gewichten wurde von B. Muckenhoupt in [Muc72a] eingeführt.

Cited by 7Open access

Spline wavelet decomposition in weighted function spaces

Ushakova, Elena P. · arXiv (Cornell University) · 2019

Battle-Lemarie wavelet systems of natural orders are established in the paper. The main result of the work is decomposition theorem in Besov and Triebel-Lizorkin spaces with local Muckenhoupt weights, which is performed in terms of bases generated by the systems of such a type. Battle-Lemarie wavelets are splines and suit very well for the study of integration operators.

Cited by 0Open access

Admissible function spaces for weighted Sobolev inequalities

T. V. Anoop, Nirjan Biswas, Ujjal Das · Communications on Pure &amp Applied Analysis · 2021

<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ k,N\in \mathbb{N} $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M2">\begin{document}$ 1\le k\le N $\end{document}</tex-math></inline-formula> and let <inline-formula><tex-math id="M3">\begin{document}$ \Omega = \Omega_1 \times \Omega_2 $\end{document}</tex-math></inline-formula> be an open set in <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{R}^k \times \mathbb{R}^{N-k} $\end{document}</tex-math></inline-formula>. For <inline-formula><tex-math id="M5">\begin{document}$ p\in (1,\infty) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ q \in (0,\infty), $\end{document}</tex-math></inline-formula> we consider the following weighted Sobolev type inequality: <p style='text-indent:20px;'><disp-formula><label/><tex-math id="FE1">\begin{document}$\begin{align} \int_{\Omega} |g_1(y)||g_2(z)| |u(y,z)|^q \, {\rm d}y {\rm d}z \leq C \left( \int_{\Omega} | \nabla u(y,z) |^p \, {\rm d}y {\rm d}z \right)^{\frac{q}{p}}, \quad \forall \, u \in \mathcal{C}^1_c(\Omega), \\(0.1)\end{align}$\end{document}</tex-math></disp-formula> <p style='text-indent:20px;'>for some <inline-formula><tex-math id="M7">\begin{document}$ C&gt;0 $\end{document}</tex-math></inline-formula>. Depending on the values of <inline-formula><tex-math id="M8">\begin{document}$ N,k,p,q $\end{document}</tex-math></inline-formula> we have identified various pairs of Lorentz spaces, Lorentz-Zygmund spaces and weighted Lebesgue spaces for <inline-formula><tex-math id="M9">\begin{document}$ (g_1, g_2) $\end{document}</tex-math></inline-formula> so that (0.1) holds. Furthermore, we give a sufficient condition on <inline-formula><tex-math id="M10">\begin{document}$ g_1,g_2 $\end{document}</tex-math></inline-formula> so that the best constant in (0.1) is attained in the Beppo-Levi space <inline-formula><tex-math id="M11">\begin{document}$ \mathcal{D}^{1,p}_0(\Omega) $\end{document}</tex-math></inline-formula>-the completion of <inline-formula><tex-math id="M12">\begin{document}$ \mathcal{C}^1_c(\Omega) $\end{document}</tex-math></inline-formula> with respect to <inline-formula><tex-math id="M13">\begin{document}$\|\nabla u\|_{L p(\Omega)}$\end{document}</tex-math></inline-formula>.

Cited by 0Open access

Weighted function spaces: Convolutors, multipliers, and mollifiers

Lenny Neyt, Yoshihiro Sawano · Mathematische Nachrichten · 2026

Abstract We study smooth function spaces of Gelfand–Shilov type, with global behavior governed through a translation‐invariant Banach function space (TIBF) and localized via a weight function system. We clarify the roles of the TIBF, convolution, and pointwise multiplication in connection with the weight function system. Our primary goal is to characterize these function spaces—as well as the corresponding convolutor and multiplier spaces—through mollification. For this purpose, we introduce the moment‐wise decomposition factorization property for pairs of compactly supported smooth functions, and establish complete characterizations in terms of mollifications with these windows.

Cited by 0

Embeddings Between Weighted Ces\`aro Function Spaces

\"Unver, Tu\u{g}\c{c}e · arXiv (Cornell University) · 2019

In this paper, we give the characterization of the embeddings between weighted Ces\`aro function spaces. The proof is based on the duality technique, which reduces this problem to the characterizations of some direct and reverse Hardy-type inequalities and iterated Hardy-type inequalities.

Cited by 0Open access

Boundedness of weighted iterated Hardy-type operators involving suprema from weighted Lebesgue spaces into weighted Cesàro function spaces

Rza Mustafayev, Nevin Bilgiçli · arXiv (Cornell University) · 2020

The boundedness of the weighted iterated Hardy-type operators \\(T_{u,b}\\) and \\(T_{u,b}^*\\) involving suprema from weighted Lebesgue space \\(L_p(v)\\) into weighted Cesàro function spaces \\({\\operatorname{Ces}}_{q}(w,a)\\) are characterized. These results allow us to obtain the characterization of the boundedness of the supremal operator \\(R_u\\) from \\(L^p(v)\\) into \\({\\operatorname{Ces}}_{q}(w,a)\\) on the cone of monotone non-increasing functions. For the convenience of the reader, we formulate the statement on the boundedness of the weighted Hardy operator \\(P_{u,b }\\) from \\(L^p(v)\\) into \\({\\operatorname{Ces}}_{q}(w,a)\\) on the cone of monotone non-increasing functions. Under additional condition on \\(u\\) and \\(b\\), we are able to characterize the boundedness of weighted iterated Hardy-type operator \\(T_{u,b}\\) involving suprema from \\(L^p(v)\\) into \\({\\operatorname{Ces}}_q(w,a)\\) on the cone of monotone non-increasing functions. At the end of the paper, as an application of obtained results, we calculate the norm of the fractional maximal function \\(M_{\\gamma}\\) from \\(\\Lambda^p(v)\\) into \\(\\Gamma^q(w)\\).

Cited by 0Open access