Related papers: Reply to Comment arXiv:0704.3529v1

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We prove the Hardy-Littlewood theorem in two dimensions for functions whose Fourier coefficients obey general monotonicity conditions and, importantly, are not necessarily positive. The sharpness of the result is given by a counterexample,…

Comment: Struggles with Survey Weighting and Regression Modeling [arXiv:0710.5005]

Comment: Struggles with Survey Weighting and Regression Modeling [arXiv:0710.5005]

Comment: Struggles with Survey Weighting and Regression Modeling [arXiv:0710.5005]

Comment: Struggles with Survey Weighting and Regression Modeling [arXiv:0710.5005]

Comment: Struggles with Survey Weighting and Regression Modeling [arXiv:0710.5005]

Motivated by G. H. Hardy's 1939 results \cite{Hardy} on functions orthogonal with respect to their real zeros $\lambda_{n}, n=1,2,... $, we will consider, within the same general conditions imposed by Hardy, functions satisfying an…

Let $1\leq p <\infty$ and $0 < q,r < \infty$. We characterize validity of the inequality for the composition of the Hardy operator, \begin{equation*} \bigg(\int_a^b \bigg(\int_a^x \bigg(\int_a^t f(s)ds \bigg)^q u(t) dt \bigg)^{\frac{r}{q}}…

We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of $\mathbb{C}.$ In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not…

Sharp multi-dimensional Hardy's inequality for the Laguerre functions of Hermite type is proved for the type parameter $\al\in[-1/2,\infty)^d$. As a consequence we obtain the corresponding result for the generalized Hermite expansions. In…

We prove that the local version of the chain rule cannot hold for the fractional variation defined in arXiv:1809.08575. In the case $n = 1$, we prove a stronger result, exhibiting a function $f \in BV^{\alpha}(\mathbb{R})$ such that $|f|…

Comment on ``On Random Scan Gibbs Samplers'' [arXiv:0808.3852]

In this note we present a version of Hardy's inequality on a measure space $(X,\mu)$ endowed with a measurable function $N\colon X\to \mathbb R$ which replaces the absolute value on $\mathbb R$ or $\mathbb R^n$, and, more generally, the…

We establishe an affine Hardy-Littlewood-Sobolev inequality concerning two different functions which is stronger than the classical Hardy-Littlewood-Sobolev inequality. Furthermore, we also prove reverse inequalities for the new…

We respond to comments in arXiv:2502.15817v2 about our article, arXiv:2412.12282. We stand by our conclusions and defend them against the criticisms.

We briefly remind references and arguments, already discussed in the past, which confute erroneous claims in arXiv:1210.5501.

A refinement of the Hardy inequality has been presented by use of superquadratic function.

We give a necessary and sufficient condition for a measure $\mu$ in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lef\'evre, Li, Queff\'elec and Rodr\'{\i}guez-Piazza \cite{LLQR}.…

In this short note, a general result concerning the positivity, under some conditions, of the coefficients of a power series is proved. This allows us to answer positively a question raised by Guo (2010) about the sign of the coefficients…