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Perturbations of isometries between C(K)-spaces

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Dutrieux Y., Kalton N.

Studia Mathematica

2005

tom 166

nr 2

181-197

We study the Gromov-Hausdorff and Kadets distances between C(K)-spaces and their quotients. We prove that if the Gromov-Hausdorff distance between C(K) and C(L) is less than 1/16 then K and L are homeomorphic. If the Kadets distance is less than one, and K and L are metrizable, then C(K) and C(L) are linearly isomorphic. For K and L countable, if C(L) has a subquotient which is close enough to C(K) in the Gromov-Hausdorff sense then K is homeomorphic to a clopen subset of L.

The Marcinkiewicz multiplier condition for bilinear operators

100%

Grafakos L., Kalton N.

Studia Mathematica

2001

tom 146

nr 2

115-156

This article is concerned with the question of whether Marcinkiewicz multipliers on $ℝ^{2n}$ 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 spaces.

Ograniczanie wyników

2 Studia Mathematica

2 Kalton N.

1 Dutrieux Y.

1 Grafakos L.

1 2005

1 2001

Wyniki wyszukiwania

Perturbations of isometries between C(K)-spaces

The Marcinkiewicz multiplier condition for bilinear operators