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Erschienen in:
Open Access 01.12.2006 | Research Article
On extrapolation blowups in the
scale
Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2006
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Abstract
Yano's extrapolation theorem dated back to 1951 establishes boundedness properties of a subadditive operator
acting continuously in
for
close to
and/or taking
into
as
and/or
with norms blowing up at speed
and/or
,
. Here we give answers in terms of Zygmund, Lorentz-Zygmund and small Lebesgue spaces to what happens if
as
. The study has been motivated by current investigations of convolution maximal functions in stochastic analysis, where the problem occurs for
. We also touch the problem of comparison of results in various scales of spaces.
acting continuously in
for
close to
and/or taking
into
as
and/or
with norms blowing up at speed
and/or
,
. Here we give answers in terms of Zygmund, Lorentz-Zygmund and small Lebesgue spaces to what happens if
as
. The study has been motivated by current investigations of convolution maximal functions in stochastic analysis, where the problem occurs for
. We also touch the problem of comparison of results in various scales of spaces.