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1

Spectral decompositions in Banach spaces and the Hilbert transform

100%

Gillespie T. A.

Banach Center Publications

|

1997

|

tom 38

|

nr 1

105-118

EN

This paper gives a survey of some recent developments in the spectral theory of linear operators on Banach spaces in which the Hilbert transform and its abstract analogues play a fundamental role.

2

Spectral decompositions and harmonic analysis on UMD spaces

63%

Berkson E., Gillespie T. A.

Studia Mathematica

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1994-1995

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tom 112

|

nr 1

13-49

EN

We develop a spectral-theoretic harmonic analysis for an arbitrary UMD space X. Our approach utilizes the spectral decomposability of X and the multiplier theory for $L_X^p$ to provide on the space X itself analogues of the classical themes embodied in the Littlewood-Paley Theorem, the Strong Marcinkiewicz Multiplier Theorem, and the M. Riesz Property. In particular, it is shown by spectral integration that classical Marcinkiewicz multipliers have associated transforms acting on X.

3

$L^{p}$-Multiplier transference induced by representations in Hilbert space

51%

Berkson E., Gillespie T. A., Muhly P. S.

Studia Mathematica

|

1989

|

tom 94

|

nr 1

51-61

4

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The spectral decomposition of weighted shifts and the $A^p$ condition

51%

Berkson E., Gillespie T. A.

Colloquium Mathematicum

|

1990

|

tom 60-61

|

nr 2

507-518

Ograniczanie wyników

2 Studia Mathematica

1 Banach Center Publications

1 Colloquium Mathematicum

4 Gillespie T. A.

3 Berkson E.

1 Muhly P. S.

1 1997

1 1994

1 1990

1 1989

Spectral decompositions in Banach spaces and the Hilbert transform

Spectral decompositions and harmonic analysis on UMD spaces

$L^{p}$-Multiplier transference induced by representations in Hilbert space

The spectral decomposition of weighted shifts and the $A^p$ condition