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Benoît F. Sehba

Publications and source records attributed to Benoît F. Sehba.

18 recordsLinked to original sources
arXiv2026

Factorization and Atomic Decomposition in Hardy-Orlicz Spaces on the Upper Half-Plane with Applications to Hankel Operators

In this work, we establish a strong factorization for Hardy-Orlicz spaces on the upper half-plane. We show that the product of two functions belonging respectively to Hardy-Orlicz spaces $H^{Φ_{1}}$ and $H^{Φ_{2}}$ lies in a third space $H^{Φ_{3}}$, and every holomorphic function in $H^{Φ_{3}}$ admits such a decomposition. We then provide an atomic decomposition for certain Hardy-Orlicz spaces, which allows us to describe the topological dual of these spaces when the associated function is concave. Finally, these results are applied to the study of the continuity of the Hankel operators in this setting.

math.CA↗
arXiv2026

On some inequalities for weighted products and ratios of the sine function

We introduce a reflection-substitution technique for sine inequalities that yields, via Hölder's inequality and its reverse, $2^{n-1}$ distinct upper bounds for products and lower bounds for ratios of weighted sines. The comparison between bounds reduces to simple sign conditions on linear combinations of the variables. We fully classify the two- and three-dimensional cases, providing explicit dominance criteria with detailed examples for each signature.

math.GM↗
arXiv2026

Weighted Product Inequalities for the Sine Function: A Gamma-Function Approach and Sharp Comparisons

Using the log-convexity of the Gamma function and Euler's reflection formula, we give a new proof of a classical weighted sine product inequality. Two different parameter choices yield two competing upper bounds for the same product. We determine precisely, via algebraic criteria, when one bound is sharper than the other. Explicit results are given for the general $n$-angle case, the $2n$-angle case, and for two and three angles. Several sharp corollaries are derived, including $\sin(πx)\leq \sin(2πx(1-x))$.

math.GM↗
arXiv2020

About a conjecture of Lieb-Solovej

Very recently, E. H. Lieb and J. P. Solovej stated a conjecture about the constant of embedding between two Bergman spaces of the upper-half plane. A question in relation with a Werhl-type entropy inequality for the affine $AX+B$ group. More precisely, that for any holomorphic function $F$ on the upper-half plane $Π^+$, $$\int_{Π^+}|F(x+iy)|^{2s}y^{2s-2}dxdy\le \frac{π^{1-s}}{(2s-1)2^{2s-2}}\left(\int_{Π^+}|F(x+iy)|^2 dxdy\right)^s $$ for $s\ge 1$, and the constant $\frac{π^{1-s}}{(2s-1)2^{2s-2}}$ is sharp. We prove differently that the above holds whenever $s$ is an integer and we prove that it holds when $s\rightarrow\infty$. We also prove that when restricted to powers of the Bergman kernel, the conjecture holds. We next study the case where $s$ is close to $1.$ Hereafter, we transfer the conjecture to the unit disc where we show that the conjecture holds when restricted to analytic monomials. Finally, we overview the bounds we obtain in our attempts to prove the conjecture.

math.CV↗
arXiv2020

Martingale Hardy-Amalgam Spaces: Atomic decompositions and duality

In this paper, we introduce the notion of martingale Hardy-amalgam spaces: $ H^s_{p,q},\,\,\mathcal{Q}_{p,q}$ and $\mathcal{P}_{p,q}$. We present two atomic decompositions for these spaces. The dual space of $H^s_{p,q}$ for $0<p\le q\le 1$ is shown to be a Campanato-type space.

math.CA↗
arXiv2018

Sharp off-diagonal weighted norm estimates for the Bergman projection

We prove that for $1<p\le q<\infty$, $qp\geq {p'}^2$ or $p'q'\geq q^2$, $\frac{1}{p}+\frac{1}{p'}=\frac{1}{q}+\frac{1}{q'}=1$, $$\|ωP_α(f)\|_{L^p(\mathcal{H},y^{α+(2+α)(\frac{q}{p}-1)}dxdy)}\le C_{p,q,α}[ω]_{B_{p,q,α}}^{(\frac{1}{p'}+\frac{1}{q})\max\{1,\frac{p'}{q}\}}\|ωf\|_{L^p(\mathcal{H},y^αdxdy)}$$ where $P_α$ is the weighted Bergman projection of the upper-half plane $\mathcal{H}$, and $$[ω]_{B_{p,q,α}}:=\sup_{I\subset \mathbb{R}}\left(\frac{1}{|I|^{2+α}}\int_{Q_I}ω^{q}dV_α\right)\left(\frac{1}{|I|^{2+α}}\int_{Q_I}ω^{-p'}dV_α\right)^{\frac{q}{p'}},$$ with $Q_I=\{z=x+iy\in \mathbb{C}: x\in I, 0<y<|I|\}$.

math.CA↗
arXiv2017

The Duren-Carleson theorem in tube domains over symmetric cones

In the setting of tube domains over symmetric cones, $T_Ω$, we study the characterization of the positive Borel measures $μ$ for which the Hardy space $H^p$ is continuously embedded into the Lebesgue space $L^q (T_Ω, dμ)$, $0<p<q<\infty.$ Extending a result due to Blasco for the unit disc, we reduce the problem to standard measures. We obtain that a Hardy space $H^{p}$, $1\leq p < \infty,$ embeds continuously in weighted Bergman spaces with larger exponents. Finally we use this result to characterize multipliers from $H^{2m}$ to Bergman spaces for every positive integer $m$.

math.CA↗
arXiv2017

An embedding relation for bounded mean oscillation on rectangles

In the two-parameter setting, we say a function belongs to the mean little $BMO$, if its mean over any interval and with respect to any of the two variables has uniformly bounded mean oscillation. This space has been recently introduced by S. Pott and the author in relation with the multiplier algebra of the product $BMO$ of Chang-Fefferman. We prove that the Cotlar-Sadosky space of functions of bounded mean oscillation $bmo(\mathbb{T}^N)$ is a strict subspace of the mean little $BMO$.

math.CA↗
arXiv2017

Some Carleson measures for the Hilbert-Hardy space of tube domains over symmetric cones

In this note, we obtain a full characterization of radial Carleson measures for the Hilbert-Hardy space on tube domains over symmetric cones. For large derivatives, we also obtain a full characterization of the measures for which the corresponding embedding operator is continuous. Restricting to the case of light cones of dimension three, we prove that by freezing one or two variables, the problem of embedding derivatives of the Hilbert-Hardy space into Lebesgue spaces reduces to the characterization of Carleson measures for Hilbert-Bergman spaces of the upper-half plane or the product of two upper-half planes.

math.CA↗
arXiv2017

Weighted boundedness of maximal functions and fractional Bergman operators

The aim of this paper is to study two-weight norm inequalities for fractional maximal functions and fractional Bergman operator defined on the upper-half space. Namely, we characterize those pairs of weights for which these maximal operators satisfy strong and weak type inequalities. Our characterizations are in terms of Sawyer and Békollé-Bonami type conditions. We also obtain a $Φ$-bump characterization for these maximal functions, where $Φ$ is a Orlicz function. As a consequence, we obtain two-weight norm inequalities for fractional Bergman operators. Finally, we provide some sharp weighted inequalities for the fractional maximal functions.

math.CA↗
arXiv2017

Maximal functions and measures on the upper-half plane

We study weighted boundedness of Hardy-Littlewood-type maximal function involving Orlicz functions. We also obtain some sufficient conditions for the weighted boundedness of the Hardy-Littlewood maximal function of the upper-half plane.

math.CA↗
arXiv2016

Derivatives characterization of Bergman-Orlicz spaces and applications

It is well known that a function is in a Bergman space of the unit ball if and only if it satisfies some Hardy-type inequalities. We extend this fact to Bergman-Orlicz spaces. As applications, we obtain Gustavsson-Peetre interpolation of two Bergman-Orlicz spaces and we completely characterize symbols of bounded or compact Cesàro-type operators on Bergman-Orlicz spaces, extending known results for classical weighted Bergman spaces.

math.CA↗
arXiv2014

Maximal function and Carleson measures in Békollé-Bonami weights

Let $ω$ be a Békollé-Bonami weight. We give a complete characterization of the positive measures $μ$ such that $$\int_{\mathcal H}|M_ωf(z)|^qdμ(z)\le C\left(\int_{\mathcal H}|f(z)|^pω(z)dV(z)\right)^{q/p}$$ and $$μ\left(\{z\in \mathcal H: Mf(z)>λ\}\right)\le \frac{C}{λ^q}\left(\int_{\mathcal H}|f(z)|^pω(z)dV(z)\right)^{q/p}$$ where $M_ω$ is the weighted Hardy-Littlewood maximal function on the upper-half plane $\mathcal H$, and $1\le p,q<\infty$.

math.CA↗