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In 2006 Carbery raised a question about an improvement on the naive norm inequality $|f+g|_p^p leq 2^{p-1}(|f|_p^p + |g|_p^p)$ for two functions in $L^p$ of any measure space. When $f=g$ this is an equality, but when the supports of $f$ and $g$ are disjoint the factor $2^{p-1}$ is not needed. Carberys question concerns a proposed interpolation between the two situations for $p>2$. The interpolation parameter measuring the overlap is $|fg|_{p/2}$. We prove an inequality of this type that is stronger than the one Carbery proposed. Moreover, our stronger inequalities are valid for all $p$.
We study $L^p$ inequalities that sharpen the triangle inequality for sums of $N$ functions in $L^p$.
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 which furt
The paper studies the sampling discretization problem for integral norms on subspaces of $L^p(mu)$. Several close to optimal results are obtained on subspaces for which certain Nikolskii-type inequality is valid. The problem of norms discretization i
Log-concave distributions include some important distributions such as normal distribution, exponential distribution and so on. In this note, we show inequalities between two Lp-norms for log-concave distributions on the Euclidean space. These inequa
In this paper we extend classical Titchmarsh theorems on the Fourier transform of H$ddot{text{o}}$lder-Lipschitz functions to the setting of harmonic $NA$ groups, which relate smoothness properties of functions to the growth and integrability of thei