Related papers: Approximation properties for $p$-adic symplectic g…

The approximation in the sense of $\Gamma$-convergence of nonisotropic Griffith-type functionals, with $p-$growth ($p>1$) in the symmetrized gradient, by means of a suitable sequence of non-local convolution type functionals defined on…

We prove an $L^p$-spectral multiplier theorem for sub-Laplacians on Heisenberg type groups under the sharp regularity condition $s>d\left|1/p-1/2\right|$, where $d$ is the topological dimension of the underlying group. Our approach relies…

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…

We study Fourier multiplier operators associated with symbols $\xi\mapsto \exp(i\lambda\phi(\xi/|\xi|))$, where $\lambda$ is a real number and $\phi$ is a real-valued $C^\infty$ function on the standard unit sphere…

Let k be a field, G a smooth connected linear algebraic group and X a homogeneous space of G over k, such that the geometric stabilizers are extensions of a smooth group of multiplicative type by a smooth connected characterfree group. If k…

Consider a lattice $\Gamma$ in a group $G = SL_2(\R), SO(1,n), SU(1,n)$, $SL_2(\Q_p)$. We discuss actions of $\Gamma$ by affine isometric transformations of Hilbert spaces. We show that for irreducible affine isometric action of $G$ its…

For a Tychonoff space $X$, denote by $\mathfrak{P}$ the family of topological properties $\mathcal{P}$ of being a convergent sequence or being a compact, sequentially compact, countably compact, pseudocompact and functionally bounded subset…

We show that for a locally compact group $G$, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra $A(G)$ satisfies a completely bounded version Pisier's similarity property with…

We show that the classifying space of a $p$-local compact group is approximated by a telescope of classifying spaces of $p$-local finite groups. This result has numerous implications, like a Stable Elements Theorem for $p$-local compact…

Fixed a Banach operator ideal $\mathcal A$, we introduce and investigate two new approximation properties, which are strictly weaker than the bounded approximation property (BAP) for $\mathcal A$ of Lima, Lima and Oja (2010). We call them…

We show that strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic.

In this paper, we investigate the $H^p(G) \rightarrow L^p(G)$, $0< p \leq 1$, boundedness of multiplier operators defined via group Fourier transform on a graded Lie group $G$, where $H^p(G)$ is the Hardy space on $G$. Our main result…

We study the homological properties of Schur algebras $S(p, 2p)$ over a field $k$ of positive characteristic $p$, focusing on their interplay with the representation theory of quotients of group algebras of symmetric groups via Schur-Weyl…

For a locally compact group $G$ and $p \in (1,\infty)$, we define $B_p(G)$ to be the space of all coefficient functions of isometric representations of $G$ on quotients of subspaces of $L_p$ spaces. For $p =2$, this is the usual…

We prove that for certain subsets $M \subseteq \mathbb{R}^N$, $N \geqslant 1$, the Lipschitz-free space $\mathcal{F}(M)$ has the metric approximation property (MAP), with respect to any norm on $\mathbb{R}^N$. In particular,…

Let $G$ be a locally compact group with an open subgroup $H$ with the Kunze-Stein property, and let $\pi$ be a unitary representation of $H$. We show that the representation $\widetilde{\pi}$ of $G$ induced from $\pi$ is an…

Several new inequalities for moduli of smoothness and errors of the best approximation of a function and its derivatives in the spaces $L_p$, $0<p<1$, are obtained. For example, it is shown that for any $0<p<1$ and $k,\,r\in \mathbb{N}$ one…

Our main result is that the simple Lie group $G=Sp(n,1)$ acts properly isometrically on $L^p(G)$ if $p>4n+2$. To prove this, we introduce property $({\BP}_0^V)$, for $V$ be a Banach space: a locally compact group $G$ has property…

We develop a new method, based on non-vanishing of second cohomology groups, for proving the failure of lifting properties for full C$^*$-algebras of countable groups with (relative) property (T). We derive that the full C$^*$-algebras of…

We study the $L^p$ mapping properties of the strong spherical maximal function, which is a multiparameter generalisation of Stein's spherical maximal function. We show that this operator is bounded on $L^p$ for $p > 2$ in all dimensions $n…