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Abstract.We prove analogues of the Brown-Halmos and Nehari theorems on
the norms of Toeplitz and Hankel operators, respectively, acting on subspaces
of Hardy type of reflexive rearrangement-invariant… (More)

We show that if the Hardy–Littlewood maximal operator is bounded on a separable Banach function space \(X(\mathbb{R}^{n})\) and on its associate space \(X^{\prime}(\mathbb{R}^{n})\), then a… (More)

Let $$\Gamma $$Γ be a rectifiable Jordan curve, let X and Y be two reflexive Banach function spaces over $$\Gamma $$Γ such that the Cauchy singular integral operator S is bounded on each of them, and… (More)

We prove that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$ and a maximally modulated… (More)

We show that the Hardy-Littlewood maximal operator is bounded on a reflexive variable Lebesgue space $L^{p(\cdot)}$ over a space of homogeneous type $(X,d,\mu)$ if and only if it is bounded on its… (More)

This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project PEst-OE/MAT/UIO297/2014 (Centro de Matemdtica e… (More)

AbstractWe prove Szegö’s strong limit theorem for Toeplitz determinants with a symbol
having a nonstandard smoothness. We assume that the symbol belongs to the Wiener algebra
and, moreover, the… (More)

Abstract Let MX,w(ℝ) denote the algebra of the Fourier multipliers on a separable weighted Banach function space X(ℝ,w).We prove that if the Cauchy singular integral operator S is bounded on X(ℝ, w),… (More)