Variants of the Maurey–Rosenthal Theorem for Quasi Köthe Function Spaces

Variants of the Maurey–Rosenthal Theorem for Quasi Köthe Function Spaces The Maurey–Rosenthal theorem states that each bounded and linear operator T from a quasi normed space E into some Lp(ν)(0<p<r<∞) which satisfies a vector-valued norm inequality $$\left\| {\left( {\sum {\left| {Tx_k } \right|} ^r } \right)^{1/r} } \right\|_{L_p } \leqslant \left( {\sum {\left\| {x_k } \right\|_E^r } } \right)^{1/r} {\text{ for all }}x_1 , \ldots ,x_n \in E,$$ even allows a weighted norm inequality: there is a function 0≤w∈L 0(ν) such that $$\left( {\int {\frac{{\left| {Tx} \right|^r }}{w}dv} } \right)^{1/r} \leqslant \left\| x \right\|_E {\text{ for all }}x \in E.$$ Continuing the work of Garcia-Cuerva and Rubio de Francia we give several scalar and vector-valued variants of this fundamental result within the framework of quasi Köthe function spaces X(ν) over measure spaces. They are all special cases of our main result (Theorem 2) which extends the Maurey–Rosenthal cycle of ideas to the case of homogeneous operators between vector spaces being homogeneously representable in quasi Köthe function spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Variants of the Maurey–Rosenthal Theorem for Quasi Köthe Function Spaces

Loading next page...
 
/lp/springer_journal/variants-of-the-maurey-rosenthal-theorem-for-quasi-k-the-function-Ycl3uGLfNZ
Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2001 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1011466509838
Publisher site
See Article on Publisher Site

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial