When is the Haar measure a Pietsch measure for nonlinear mappings?

We show that, as in the linear case, the normalized Haar measure on a compact topological group $G$ is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of $C(G)$. This answers a question posed to the authors by J. Diestel. We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section some problems are proposed

Multiplicative structures of hypercyclic functions for convolution operators

In this note, it is proved the existence of an infinitely generated multiplicative group consisting of entire functions that are, except for the constant function 1, hypercyclic with respect to the convolution operator associated to a given entire function of subexponential type. A certain stability under multiplication is also shown for compositional hypercyclicity on complex domains.Comment: 12 page

Dynamics of multidimensional Césaro operators

[EN] We study the dynamics of the multi-dimensional Cesar degrees integral operator on L-P (I-n), for I the unit interval, 1 = 2, that is defined as C(f)(x(1),...,x(n)) = 1/x(1)x(2)...x(n) integral(x1)(0) ... integral(x1)(0) f(u(1),...,u(n))du(1)...du(n) for f is an element of L-p(I-n). This operator is already known to be bounded. As a consequence of the Eigenvalue Criterion, we show that it is hypercyclic as well. Moreover, we also prove that it is Devaney chaotic and frequently hypercyclic.The first author was supported by MEC, grant MTM201675963-P. The third author was supported by grant MTM2015-65825-P.Conejero, JA.; Mundayadan, A.; Seoane-Sepúlveda, JB. (2019). Dynamics of multidimensional Césaro operators. Bulletin of the Belgian Mathematical Society Simon Stevin. 26(1):11-20. http://hdl.handle.net/10251/159145S112026

Sharp values for the constants in the polynomial Bohnenblust-Hille inequality

In this paper we prove that the complex polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb C}^2$ is exactly $\sqrt[4]{\frac{3}{2}}$. We also give the exact value of the real polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb R}^2$. Finally, we provide lower estimates for the real polynomial Bohnenblust-Hille constant for polynomials in ${\mathbb R}^2$ of higher degrees.Comment: 16 page