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Higher-Order Partial Differentiation

Noboru Endou, Hiroyuki Okazaki, Yasunari Shidama (2012)

Formalized Mathematics

In this article, we shall extend the formalization of [10] to discuss higher-order partial differentiation of real valued functions. The linearity of this operator is also proved (refer to [10], [12] and [13] for partial differentiation).

Hilbert inequality for vector valued functions

Namita Das, Srinibas Sahoo (2011)

Archivum Mathematicum

In this paper we consider a class of Hankel operators with operator valued symbols on the Hardy space Ξ 2 ( 𝕋 ) where Ξ is a separable infinite dimensional Hilbert space and showed that these operators are unitarily equivalent to a class of integral operators in L 2 ( 0 , ) Ξ . We then obtained a generalization of Hilbert inequality for vector valued functions. In the continuous case the corresponding integral operator has matrix valued kernels and in the discrete case the sum involves inner product of vectors in the...

Hilbert space factorization and Fourier type of operators

Aicke Hinrichs (2001)

Studia Mathematica

It is an open question whether every Fourier type 2 operator factors through a Hilbert space. We show that at least the natural gradations of Fourier type 2 norms and Hilbert space factorization norms are not uniformly equivalent. A corresponding result is also obtained for a number of other sequences of ideal norms instead of the Fourier type 2 gradation including the Walsh function analogue of Fourier type. Our main tools are ideal norms and random matrices.

Hilbert transform, Toeplitz operators and Hankel operators and invariant A∞ weights.

Sergei Treil, Alexander Volberg, Dechao Zheng (1997)

Revista Matemática Iberoamericana

In this paper, several sufficient conditions for boundedness of the Hilbert transform between two weighted Lp-spaces are obtained. Invariant A∞ weights are obtained. Several characterizations of invariant A∞ weights are given. We also obtain some sufficient conditions for products of two Toeplitz operators of Hankel operators to be bounded on the Hardy space of the unit circle using Orlicz spaces and Lorentz spaces.

Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on complete pseudoconvex Reinhardt domains

Mehmet Çelik, Yunus E. Zeytuncu (2017)

Czechoslovak Mathematical Journal

On complete pseudoconvex Reinhardt domains in 2 , we show that there is no nonzero Hankel operator with anti-holomorphic symbol that is Hilbert-Schmidt. In the proof, we explicitly use the pseudoconvexity property of the domain. We also present two examples of unbounded non-pseudoconvex domains in 2 that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols. In the first example the Bergman space is finite dimensional. However, in the second example the Bergman space is infinite...

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