Displaying similar documents to “Littlewood functions, Hankel multipliers and power bounded operators on a Hilbert space”

Multipliers of sequence spaces

Raymond Cheng, Javad Mashreghi, William T. Ross (2017)

Concrete Operators

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This paper is selective survey on the space lAp and its multipliers. It also includes some connections of multipliers to Birkhoff-James orthogonality

Multiplier operators on product spaces

Hung Viet Le (2002)

Studia Mathematica

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The author proves the boundedness for a class of multiplier operators on product spaces. This extends a result obtained by Lung-Kee Chen in 1994.

Multipliers on a Hilbert Space of Functions on R

Petkova, Violeta (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 42A45. For a Hilbert space H ⊂ L1loc(R) of functions on R we obtain a representation theorem for the multipliers M commuting with the shift operator S. This generalizes the classical result for multipliers in L2(R) as well as our previous result for multipliers in weighted space L2ω(R). Moreover, we obtain a description of the spectrum of S.

Distinctness of spaces of Lorentz-Zygmund multipliers

Kathryn E. Hare, Parasar Mohanty (2005)

Studia Mathematica

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We study the spaces of Lorentz-Zygmund multipliers on compact abelian groups and show that many of these spaces are distinct. This generalizes earlier work on the non-equality of spaces of Lorentz multipliers.

Schur and operator multipliers

Ivan G. Todorov, Lyudmila Turowska (2010)

Banach Center Publications

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The present article is a survey of known results on Schur and operator multipliers. It starts with the classical description of Schur multipliers due to Grothendieck, followed by a discussion of measurable Schur multipliers and a generalisation of Grothendieck's Theorem due to Peller. Thereafter, a non-commutative version of Schur multipliers, called operator multipliers and introduced by Kissin and Schulman, is discussed, and a characterisation extending the description in the commutative...

The Marcinkiewicz multiplier condition for bilinear operators

Loukas Grafakos, Nigel J. Kalton (2001)

Studia Mathematica

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This article is concerned with the question of whether Marcinkiewicz multipliers on ℝ 2 n give rise to bilinear multipliers on ℝⁿ × ℝⁿ. We show that this is not always the case. Moreover, we find necessary and sufficient conditions for such bilinear multipliers to be bounded. These conditions in particular imply that a slight logarithmic modification of the Marcinkiewicz condition gives multipliers for which the corresponding bilinear operators are bounded on products of Lebesgue and Hardy...

Hankel multipliers and transplantation operators

Krzysztof Stempak, Walter Trebels (1997)

Studia Mathematica

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Connections between Hankel transforms of different order for L p -functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated.

Some remarks on Toeplitz multipliers and Hankel matrices

Aleksander Pełczyński, Fyodor Sukochev (2006)

Studia Mathematica

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Consider the set of all Toeplitz-Schur multipliers sending every upper triangular matrix from the trace class into a matrix with absolutely summable entries. We show that this set admits a description completely analogous to that of the set of all Fourier multipliers from H₁ into ℓ₁. We characterize the set of all Schur multipliers sending matrices representing bounded operators on ℓ₂ into matrices with absolutely summable entries. Next, we present a result (due to G. Pisier) that the...

Endpoint bounds of square functions associated with Hankel multipliers

Jongchon Kim (2015)

Studia Mathematica

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We prove endpoint bounds for the square function associated with radial Fourier multipliers acting on L p radial functions. This is a consequence of endpoint bounds for a corresponding square function for Hankel multipliers. We obtain a sharp Marcinkiewicz-type multiplier theorem for multivariate Hankel multipliers and L p bounds of maximal operators generated by Hankel multipliers as corollaries. The proof is built on techniques developed by Garrigós and Seeger for characterizations of...