Pablo Rocha

activity

20222026

collaborators

11 papers

math.FA2026

A note on variable (Hardy-)Lorentz spaces

Pablo Rocha

The purpose of this note is to establish further properties of the variable Lorentz spaces $L^{p (\cdot), q (\cdot)} (R^{n})$ introduced by L. Ephremidze, V. Kokilas…

math.FA2025

Estimates for convolution operators on Hardy spaces associated with ball quasi-Banach function spaces

Pablo Rocha

Let $0 \leq α < n$ , $N \in N$ , and let $X$ and $Y$ be ball quasi-Banach function spaces on $R^{n}$ . We consider operators $T_{α}$ defined by convolution with kernels o…

math.CA2025

Estimates for Riesz potential on weighted variable Hardy spaces revisited

Pablo Rocha

In [Math. Ineq. \& appl., Vol 26 (2) (2023), 511-530] and [Period. Math. Hung., 89 (1) (2024), 116-128], the present author proved that the Riesz potential $I_{α}$ extends to a bound…

math.CA2025

Fractional series operators on $Z^{n}$

Pablo Rocha

For $0 \leq α < n$ and $m \in N \cap (1 - \frac{α}{n}, \infty)$ , we introduce a class of fractional series operators $T_{α, m}$ defined on $Z^{n}$ which are generat…

math.CA2025

The $H^{p} (Z^{n}) - H^{q} (Z^{n})$ boundedness of the discrete Riesz potential

Pablo Rocha

In [J. Class. Anal., vol. 26 (1) (2025), 63-76], we proved that the discrete Riesz potential $I_{α}$ is a bounded operator $H^{p} (Z^{n}) \to H^{q} (Z^{n})$ for $\frac{n-1}{n…

math.CA2025

Variable Calderón-Hardy spaces on the Heisenberg group

Pablo Rocha

Let $H^{n}$ be the Heisenberg group and $Q = 2 n + 2$ . For $1 < q < \infty$ , $γ > 0$ and an exponent function $p (\cdot)$ on $H^{n}$ , which satisfy log-Hölder conditions…

math.CA2025

Calderón-Hardy type spaces and the Heisenberg sub-Laplacian

Pablo Rocha

For $0 < p \leq 1 < q < \infty$ and $γ > 0$ , we introduce the Calderón-Hardy spaces $H_{q, γ}^{p} (H^{n})$ on the Heisenberg group $H^{n}$ , and show for e…

math.CA2024

A molecular decomposition for $H^{p} (Z^{n})$

Pablo Rocha

In this work, for the range $\frac{n - 1}{n} < p \leq 1$ , we give a molecular reconstruction theorem for $H^{p} (Z^{n})$ . As an application of this result and the atomic decompos…

math.CA2024

Fractional type operators on the Heisenberg group

Pablo Rocha

Let $ρ (\cdot)$ be the Koranyi norm on the Heisenberg group $H^{n} \equiv (R^{2 n} \times R, \cdot)$ defined by \[ ρ(x,t) = \left( |x|^{4} + 16 t^{2…

math.CA2024

Convolution operators and variable Hardy spaces on the Heisenberg group

Pablo Rocha

Let $H^{n}$ be the Heisenberg group. For $0 \leq α < Q = 2 n + 2$ and $N \in N$ we consider exponent functions $p (\cdot) : H^{n} \to (0, + \infty)$ , which satis…

math.CA2022

Fractional series operators on discrete Hardy spaces

Pablo Rocha

We estudy the $H^{p} (Z)$ - $ℓ^{q} (Z)$ boundedness of the fractional series operator $T_{γ}$ given by \[ (T_γb)(j) = \sum_{i \neq \pm j} \frac{b(i)}{|i-j|^α|i+j|^…

A note on variable (Hardy-)Lorentz spaces

Estimates for convolution operators on Hardy spaces associated with ball quasi-Banach function spaces

Estimates for Riesz potential on weighted variable Hardy spaces revisited

Fractional series operators on Zn

The Hp(Zn)−Hq(Zn) boundedness of the discrete Riesz potential

Variable Calderón-Hardy spaces on the Heisenberg group

Calderón-Hardy type spaces and the Heisenberg sub-Laplacian

A molecular decomposition for Hp(Zn)

Fractional type operators on the Heisenberg group

Convolution operators and variable Hardy spaces on the Heisenberg group

Fractional series operators on discrete Hardy spaces

Fractional series operators on $Z^{n}$

The $H^{p} (Z^{n}) - H^{q} (Z^{n})$ boundedness of the discrete Riesz potential

A molecular decomposition for $H^{p} (Z^{n})$