arXiv subjects

Stefanos Lappas

Publications and source records attributed to Stefanos Lappas.

11 recordsLinked to original sources

arXiv2026

Compact sets in quasi-Banach function spaces and multilinear extrapolation of compactness on $L^{p(\cdot)}(w)$

This paper addresses a novel Riesz--Kolmogorov theorem on quasi-Banach function spaces under mild conditions and the extrapolation of multilinear compact operators in the context of weighted variable Lebesgue spaces. We establish the latter result via our Riesz--Kolmogorov theorem which yields a weighted interpolation theorem for multilinear compact operators in the variable Lebesgue setting. In proving this, we also show a weighted interpolation theorem in mixed-norm variable Lebesgue spaces. By means of our extrapolation result, we obtain new weighted compactness estimates for the commutators of multilinear $ω$-Calderón--Zygmund operators, multilinear fractional integrals and multilinear Fourier multipliers on weighted variable Lebesgue spaces. Our work generalizes several recent ones, including but not limited to those of Cao, Olivo and Yabuta in the setting of multilinear operators acting on the classical weighted Lebesgue spaces as well as the previous result by the authors in the setting of bilinear operators and variable Lebesgue spaces.

math.FA↗

arXiv2026

Factorizations for variable exponent Muckenhoupt weights

Given two variable exponent Muckenhoupt weights $w\in \mathcal{A}_{p(\cdot)}$ and $w_1\in \mathcal{A}_{p_1(\cdot)}$, we prove that for all small enough $θ>0,$ there holds that $w_0\in \mathcal{A}_{p_0(\cdot)},$ where the weight is determined by $w = w_0^{1-θ}w_1^θ$ and exponent of the weight class by $1/p(\cdot) = (1-θ)/p_0(\cdot) + θ/p_1(\cdot).$ The proof is based on a recent reverse Hölder's inequality for variable exponent Muckenhoupt weights by Cruz-Uribe and Penrod. We upgrade these factorizations to the restricted range context by using a recent transformation formula due to Nieraeth. Then, following an extrapolation of compactness scheme by Hytönen and Lappas, we provide an alternative proof of the recent extrapolation of compactness results of Lorist and Nieraeth in the context of weighted variable exponent Lebesgue spaces.

math.FA↗

arXiv2025

Extrapolation for bilinear compact operators in the variable exponent setting

We establish extrapolation of compactness for bilinear operators in the scale of weighted variable exponent Lebesgue spaces. First, we prove an abstract principle relying on the Cobos-Fernández-Cabrera-Martínez theorem. Then, as an application we deduce new compactness results for the commutators of bilinear $ω$-Calderón-Zygmund operators, bilinear fractional integrals and bilinear Fourier multipliers acting on weighted variable exponent Lebesgue spaces. Our work extends and unifies among others earlier works of the second named author together with Hytönen as well as Oikari.

math.CA↗

arXiv2025

Sharp bilinear estimates for maximal singular integrals with kernels in weighted $L^q$ spaces

In this paper, we study the boundedness properties of the (dyadic) maximal bilinear operator associated with rough homogeneous kernels on $\mathbb{R}$. We establish sharp $L^{p_1}(\mathbb{R}) \times L^{p_2}(\mathbb{R}) \to L^{p}(\mathbb{R})$ estimates in the full quasi-Banach range of exponents $1 < p_1, p_2 < \infty$ and $1/2 < p < \infty$. Our approach extends and unifies several recent contributions, including those of Honzík, the first author, and Slavíkova, as well as the second author in the bilinear and in the one-dimensional settings, by allowing the angular component $Ω$ of the kernel to belong to weighted $L^q$-spaces on $\mathbb{S}^1$.

math.CA↗

arXiv2025

Bilinear singular integral operators with kernels in weighted spaces

We establish the full quasi-Banach range of $L^{p_1}(\mathbb R) \times L^{p_2}(\mathbb R) \rightarrow L^p(\mathbb R)$ bounds for one-dimensional bilinear singular integral operators with homogeneous kernels whose restriction $Ω$ to the unit sphere $\mathbb S^1$ is supported away from the degenerate line $θ_1=θ_2$, belongs to $L^q(\mathbb S^1)$ for some $q>1$ and has vanishing integral. In fact, a more general result is obtained by dropping the support condition on $Ω$ and requiring that $Ω\in L^q(\mathbb S^1,u^q)$, where $u(θ_1,θ_2)=|θ_1-θ_2|^{-1}$ for $(θ_1,θ_2)\in \mathbb S^1$. In addition, we provide counterexamples that show the failure of the $n$-dimensional version of the previous result when $n\geq 2$, as well as the failure of its $m$-linear variant in dimension one when $m\geq 3$. The relationship of these results to (un)boundedness properties of higher-dimensional multilinear Hilbert transforms is also discussed.

math.CA↗

arXiv2024

Quantitative estimates for bounded holomorphic semigroups

In this paper we revisit the theory of one-parameter semigroups of linear operators on Banach spaces in order to prove quantitative bounds for bounded holomorphic semigroups. Subsequently, relying on these bounds we obtain new quantitative versions of two recent results of Xu related to the vector-valued Littlewood--Paley--Stein theory for symmetric diffusion semigroups.

math.FA↗

arXiv2022

Dyadic representation theorem using smooth wavelets with compact support

The representation of a general Calderón--Zygmund operator in terms of dyadic Haar shift operators first appeared as a tool to prove the $A_2$ theorem, and it has found a number of other applications. In this paper we prove a new dyadic representation theorem by using smooth compactly supported wavelets in place of Haar functions. A key advantage of this is that we achieve a faster decay of the expansion when the kernel of the general Calderón--Zygmund operator has additional smoothness.

math.CA↗

arXiv2022

Extrapolation of compactness on weighted spaces

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ for all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact on $L^{p_1}(w_1)$ for some $w_1\in A_{p_1}(\mathbb R^d)$. Then $T$ is bounded and compact on $L^p(w)$ for all $p\in(1,\infty)$ and all $w\in A_p(\mathbb R^d)$. This "compact version" of Rubio de Francia's celebrated weighted extrapolation theorem follows from a combination of results in the interpolation and extrapolation theory of weighted spaces on the one hand, and of compact operators on abstract spaces on the other hand. Moreover, generalizations of this extrapolation of compactness are obtained for operators that are bounded from one space to a different one ("off-diagonal estimates") or only in a limited range of the $L^p$ scale. As applications, we easily recover several recent results on the weighted compactness of commutators of singular integral operators, fractional integrals and pseudo-differential operators, and obtain new results about the weighted compactness of commutators of Bochner-Riesz multipliers.

math.FA↗

arXiv2021

Extrapolation of compactness on weighted spaces: Bilinear operators

In a previous paper, we obtained several "compact versions" of Rubio de Francia's weighted extrapolation theorem, which allowed us to extrapolate the compactness of linear operators from just one space to the full range of weighted Lebesgue spaces, where these operators are bounded. In this paper, we study the extrapolation of compactness for bilinear operators in terms of bilinear Muckenhoupt weights. As applications, we easily recover and improve earlier results on the weighted compactness of commutators of bilinear Calderón-Zygmund operators, bilinear fractional integrals and bilinear Fourier multipliers. More general versions of these results are recently due to Cao, Olivo and Yabuta (arXiv:2011.13191), whose approach depends on developing weighted versions of the Fréchet--Kolmogorov criterion of compactness, whereas we avoid this by relying on "softer" tools, which might have an independent interest in view of further extensions of the method.

math.FA↗

arXiv2021

Extrapolation of compactness on weighted Morrey spaces

In a previous work, "compact versions" of Rubio de Francia's weighted extrapolation theorem were proved, which allow one to extrapolate the compactness of an linear operator from just one space to the full range of weighted Lebesgue spaces, where this operator is bounded. In this paper, we extend these results to the setting of weighted Morrey spaces. As applications, we easily obtain new results on the weighted compactness of commutators of Calderón--Zygmund singular integrals, rough singular integrals and Bochner--Riesz multipliers.

math.FA↗

arXiv2020

Extrapolation of compactness on weighted spaces II: Off-diagonal and limited range estimates

In a previous paper by one of us, a "compact version" of Rubio de Francia's weighted extrapolation theorem was proved, which allows one to extrapolate the compactness of an operator from just one space to the full range of weighted spaces, where this operator is bounded. In this paper, we obtain generalizations of this extrapolation of compactness for operators that are bounded from one space to a different one ("off-diagonal estimates") or only in a limited range of the $L^p$ scale. As applications, we easily recover recent results on the weighted compactness of commutators of fractional integrals and pseudo-differential operators, and obtain new results about the weighted compactness of Bochner--Riesz multipliers.

math.FA↗