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We give a constructive proof of the factorization theorem for the weighted Hardy space in terms of multilinear Calderón-Zygmund operators. The result is also new even in the linear setting. As an application, we obtain the characterization of weighted BMO space via the weighted boundedness of commutators of the multilinear Calderón-Zygmund operators.

The fall of the doubling condition in Calderón-Zygmund theory.

Joan Verdera (2002)

Publicacions Matemàtiques

The most important results of standard Calderón-Zygmund theory have recently been extended to very general non-homogeneous contexts. In this survey paper we describe these extensions and their striking applications to removability problems for bounded analytic functions. We also discuss some of the techniques that allow us to dispense with the doubling condition in dealing with singular integrals. Special attention is paid to the Cauchy Integral.[Proceedings of the 6th International Conference on...

The form boundedness criterion for the relativistic Schrödinger operator

Vladimir Maz'ya, Igor Verbitsky (2004)

Annales de l’institut Fourier

We establish necessary and sufficient conditions on the real- or complex-valued potential $Q$ defined on $ℝ^{n}$ for the relativistic Schrödinger operator $\sqrt{- Δ} + Q$ to be bounded as an operator from the Sobolev space $W_{2}^{1 / 2} (ℝ^{n})$ to its dual $W_{2}^{- 1 / 2} (ℝ^{n})$ .

The Fourier Character Of Series With Slowly Varying Convergence Moduli

Časlav V. Stanojević (1990)

Publications de l'Institut Mathématique

The Fourier integral for a certain class of distributions

Josef Matušů (1991)

Applications of Mathematics

The aim of this paper is to derive by elementary means a theorem on the representation of certain distributions in the form of a Fourier integral. The approach chosen was found suitable especially for students of post-graduate courses at technical universities, where it is in some situations necessary to restrict a little the extent of the mathematical theory when concentrating on a technical problem.

The Fourier integral operators on Hardy spaces associated with Herz spaces

Lixia Liu, Bolin Ma, Sanyang Liu (2011)

Czechoslovak Mathematical Journal

In this paper, it is proved that the Fourier integral operators of order $m$ , with $- n < m \leq - (n - 1) / 2$ , are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces.

The Fourier transform in Lebesgue spaces

Erik Talvila (2025)

Czechoslovak Mathematical Journal

For each $f \in L^{p} (ℝ)$ ( $1 \leq p < \infty$ ) it is shown that the Fourier transform is the distributional derivative of a Hölder continuous function. For each $p$ , a norm is defined so that the space of Fourier transforms is isometrically isomorphic to $L^{p} (ℝ)$ . There is an exchange theorem and inversion in norm.

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The Convergence in L... of Singular Integrals in Harmonic Analysis and Ergodic Theory.

The Convergence Rates of Expansions in Jacobi Polynomials.

The Dirichlet-Jordan theorem for the Henstock-Fourier transform.

The discrete Fourier-Transform an Lp approximation of functions.

The divergence phenomena of interpolation type operators in $L^{p}$ space

The dual of Hardy spaces on a bounded domain in Rn.

The Dunkl transform.

The Ehrhart polynomial of a lattice $n$ -simplex.

The eigenvalues of Hermite and rational spectral differentiation matrices.

The Euler Maclaurin Expansion for the Cauchy Principal Value Integral.

The factorization of the weighted Hardy space in terms of multilinear Calderón-Zygmund operators