Related papers: A Hausdorff-Young inequality for measured groupoid…
It has been shown in "On the Hausdorff-Young theorem for commutative hypergroups" by Sina Degenfeld-Schonburg, that one can extend the domain of Fourier transform of a commutative hypergroup $K$ to $L^p(K)$ for $1\leq p \leq 2$, and the…
We calculate the norm of the Fourier operator from $L^p(X)$ to $L^q(\hat{X})$ when $X$ is an infinite locally compact abelian group that is, furthermore, compact or discrete. This subsumes the sharp Hausdorff-Young inequality on such…
In this paper we establish the $L^p$-$L^q$ boundedness of Fourier multipliers on locally compact separable unimodular groups for the range of indices $1<p\leq 2 \leq q<\infty$. Our approach is based on the operator algebras techniques. The…
The classical Hausdorff-Young inequalities for the Fourier transform acting between appropriate $L_p$ spaces are cornerstones of Fourier analysis. Here we extend it to weighted spaces of Besov or Sobolev type where the weight has the form…
This paper deals with the inequalities devoted to the comparison between the norm of a function on a compact hypergroup and the norm of its Fourier coefficients. We prove the classical Paley inequality in the setting of compact hypergroups…
The paper studies Hausdorff-Young inequalities for certain group extensions, by use of Mackey's theory. We consider the case in which the dual action of the quotient group is free almost everywhere. This result applies to yield a…
In this paper we discuss the $L^p$-$L^q$ boundedness of both spectral and Fourier multipliers on general locally compact separable unimodular groups $G$ for the range $1<p\leq q<\infty$. We prove a Lizorkin type multiplier theorem for…
We prove several results about the best constants in the Hausdorff-Young inequality for noncommutative groups. In particular, we establish a sharp local central version for compact Lie groups, and extend known results for the Heisenberg…
The main purpose of this paper is to study the validity of the Hausdorff-Young inequality for vector-valued functions defined on a non-commutative compact group. The natural context for this research is that of operator spaces. This leads…
We prove that the Hausdorff--Young inequality $\|{\widehat{f}}\|_{q(\cdot)} \leq C \|{f}\|_{p(\cdot)}$ with $q(x)=p'(1/x)$ and $p(\cdot)$ even and non-decreasing holds in variable Lebesgue spaces if and only if $p$ is a constant. However,…
Let p and q be conjugate exponents, with p in [1,2]. It is shown that the Laplace transform acts boundedly between the Lp space with unit weight on the positive real semiaxis and the Lq space weighted by a well-projected measure (a term…
The Hausdorff-Young inequality for Euclidean space, in its sharp form due to Beckner, gives an upper bound for the Fourier transform in terms of Lebesgue space norms, with an optimal constant. The extremizers have been identified by Lieb to…
In this article, we establish three fundamental Fourier inequalities: the Hausdorff-Young inequality, the Paley inequality, and the Hausdorff-Young-Paley inequality for $(l, n)$-type functions on $\mathrm{SL}(2,\mathbb{R})$. Utilizing these…
This paper studies two classical inequalities, namely the Hausdorff-Young inequality and equal-exponent Young's convolution inequality, for discrete functions supported in the binary cube $\{0,1\}^d\subset\mathbb{Z}^d$. We characterize the…
Using interpolation properties of non-commutative L^p-spaces associated with an arbitrary von Neumann algebra, we define a L^p-Fourier transform 1 <= p <= 2 on locally compact quantum groups. We show that the Fourier transform determines a…
This article presents the $L^p$-Heisenberg--Pauli--Weyl uncertainty inequality for the group Fourier transform on a class of two-step nilpotent Lie groups, specifically the M\'etivier groups. This inequality quantitatively demonstrates that…
In this paper, we generalize Young's inequality for locally compact quantum groups and obtain some results for extremal pairs of Young's inequality and extremal functions of Hausdorff-Young inequality.
Mimicking the von Neumann version of Kustermans and Vaes' locally compact quantum groups, Franck Lesieur had introduced a notion of measured quantum groupoid, in the setting of von Neumann algebras. In this article, we suppose that the…
In this article, we establish the $L^p$-Heisenberg-Pauli-Weyl uncertainty inequalities on the Laguerre hypergroup $\mathbb{K}$, the natural setting for radial analysis on the Heisenberg group. For $1 \leq p < 2$, under the condition $b >…
Young's convolution inequality provides an upper bound for the convolution of functions in terms of $L^p$ norms. It is known that for certain groups, including Heisenberg groups, the optimal constant in this inequality is equal to that for…