Searcharxiv⌕ Search

arXiv subjects

Benoit F. Sehba

Publications and source records attributed to Benoit F. Sehba.

At least 19 recordsLinked to original sources
arXiv2026

Sharp weighted norm estimates for the positive Bergman operator: the two-parameter case

We settle the two-parameter sharp weighted theory for the positive Bergman operator on the upper half-plane: we allow the exponent $\alpha$ that defines the operator to differ from the exponent $\gamma$ that defines the underlying weighted Lebesgue spaces. In this setting, we prove sharp weak-type and strong-type off-diagonal weighted inequalities, with explicit and best-possible dependence on the B\'ekoll\'e--Bonami characteristic of the weight. The key new tool is an off-diagonal extrapolation theorem, adapted to allow a change in the power of the distance to the boundary along the way.

math.CA↗
arXiv2026

Convexity of the embedding parameter sets of some analytic function spaces

In this note, we study the geometric structure of the parameter sets governing continuous embeddings between weighted Bergman-Orlicz spaces. First, for a fixed pair of growth functions, we show that the set of admissible weight exponents $(\alpha, \beta)$ is convex, provided the growth functions satisfy specific log-convexity and log-concavity conditions of the inverses. Second, we consider the dual problem where the weight exponents are fixed. We prove that the collection of growth function pairs that yield such an embedding is log-convex under a natural interpolation of their inverses. We then obtain interpolated embeddings between Bergman-Orlicz spaces.

math.CA↗
arXiv2026

A sharp logarithmic condition for the Hardy operator on $L^{1}(0,\infty)$ and $\ell^1$

The Hardy operator is not bounded on the space of integrable functions on the positive half-line and its discrete counterpart on summable sequences. we introduce a modified Hardy operator obtained by subtracting a natural corrective term, and characterize the largest subspace of integrable functions on which this modified operator maps into integrable functions. The sharp condition is a logarithmic integrability (summability) requirement whose weight reflects obstructions on both small and large scales.

math.CA↗
arXiv2024

Boundedness of the Bergman projection on some weighted mixed norm Lebesgue spaces of the upper-half space

In this paper, we prove the boundedness of the Bergman projection on weighted mixed norm spaces of the upper-half space for some weights that are constructed using the logarithm function and growth functions. Our necessary and sufficient condition is the same as in the unweighted case, that is it involves only the parameters and not the weight. We then provide some applications in terms of dual and derivative characterization, and an atomic decomposition of the corresponding Bergman spaces.

math.CA↗
arXiv2021

Dyadic Martingale Hardy-amalgam spaces: Embeddings and Duality

We present in this paper some embeddings of various dyadic martingale Hardy-amalgam spaces $H^S_{p,q},\,\, H^s_{p,q},\,\,H^*_{p,q},\,\,\mathcal{Q}_{p,q}$ and $\mathcal{P}_{p,q}$ of the real line. In the same settings, we characterize the dual of $H^s_{p,q}$ for large $p$ and $q$. We also introduce a Garsia-type space $\mathcal{G}_{p,q}$ and characterize its dual space.

math.CA↗
arXiv2016

On some equivalent definitions of $ρ$- Carleson measures on the unit ball

We give in this paper some equivalent definitions of the so called $ρ$-Carleson measures when $ρ(t)=(\log(4/t))^p(\log\log(e^4/t))^q$, $0\le p,q<\infty$. As applications, we characterize the pointwise multipliers on $LMOA(\mathbb S^n)$ and from this space to $BMOA(\mathbb S^n)$. Boundedness of the Cesàro type integral operators on $LMOA(\mathbb S^n)$ and from $LMOA(\mathbb S^n)$ to $BMOA(\mathbb S^n)$ is considered as well.

math.CA↗
arXiv2016

Boundeness of a family of Hilbert-type operators and of its Bergman-type analogue

In this note, we frst consider boundedness properties of a family of operators generalizing the Hilbert operator in the upper triangle case. In the diagonal case, we give the exact norm of these operators under some restrictions on the parameters. We secondly consider boundedness properties of a family of positive Bergman-type operators of the upper-half plane. We give necessary and sufficient conditions on the parameters under which these operators are bounded in the upper triangle case.

math.CA↗
arXiv2015

On two-weight norm estimates for multilinear fractional maximal function

We prove some Sawyer-type characterizations for multilinear fractional maximal function for the upper triangle case. We also provide some two-weight norm estimates for this operator. As one of the main tools, we use an extension of the usual Carleson Embedding that is an analogue of the P. L. Duren extension of the Carleson Embedding for measures.

math.CA↗
arXiv2015

Duality for large Bergman-Orlicz spaces and Boundedness of Hankel Operators

For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^Φ_α$, which are generalizations of classical Bergman spaces. We characterize the dual space of large Bergman-Orlicz space, and bounded Hankel operators between some Bergman-Orlicz spaces $A_α^{Φ_1}(\mathbb B^n)$ and $A_α^{Φ_2}(\mathbb B^n)$ where $Φ_1$ and $Φ_2$ are either convex or concave growth functions.

math.CA↗