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Weighted multilinear hardy operators on Herz type spaces.
Shuli Gong1, Zunwei Fu2, Bolin Ma3
1College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China.
Thescientificworldjournal
|February 11, 2014
Summary
This study investigates weighted multilinear Hardy operators on product Herz and Morrey-Herz spaces. A sufficient weight condition ensures boundedness on product Herz spaces, with extensions to Morrey-Herz spaces.
Area of Science:
- Analysis
- Functional Analysis
- Operator Theory
Background:
- Hardy operators are fundamental in analysis.
- Product Herz and Morrey-Herz spaces are important function spaces.
- Understanding operator bounds is crucial for theoretical development.
Purpose of the Study:
- To determine the boundedness of weighted multilinear Hardy operators.
- To establish conditions for operator boundedness on product Herz spaces.
- To extend these findings to product Morrey-Herz spaces.
Main Methods:
- Analysis of weighted multilinear Hardy operators.
- Characterization of weight functions for boundedness.
- Techniques from harmonic analysis and function spaces.
Main Results:
- A sufficient condition for the boundedness of weighted multilinear Hardy operators on product Herz spaces is established.
- This condition is shown to be necessary under specific assumptions.
- The results are successfully extended to the product Morrey-Herz spaces.
Conclusions:
- The paper provides precise conditions for the boundedness of weighted multilinear Hardy operators.
- The findings contribute to the theory of function spaces and operator inequalities.
- The extension to Morrey-Herz spaces broadens the applicability of the results.
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