| Title:
|
Integral and derivative operators of functional order on generalized Besov and Triebel-Lizorkin spaces in the setting of spaces of homogeneous type (English) |
| Author:
|
Hartzstein, Silvia I. |
| Author:
|
Viviani, Beatriz E. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
723-754 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the setting of spaces of homogeneous-type, we define the Integral, $I_{\phi}$, and Derivative, $D_{\phi}$, operators of order $\phi$, where $\phi$ is a function of positive lower type and upper type less than $1$, and show that $I_{\phi}$ and $D_{\phi}$ are bounded from Lipschitz spaces $\Lambda^{\xi}$ to $\Lambda^{\xi \phi}$ and $\Lambda^{\xi/\phi}$ respectively, with suitable restrictions on the quasi-increasing function $\xi$ in each case. We also prove that $I_{\phi}$ and $D_{\phi}$ are bounded from the generalized Besov $\dot{B}_{p}^{\psi, q}$, with $1 \leq p, q < \infty $, and Triebel-Lizorkin spaces $\dot{F}_{p}^{\psi, q}$, with $1 < p, q < \infty $, of order $\psi$ to those of order $\phi \psi$ and $\psi/\phi$ respectively, where $\psi$ is the quotient of two quasi-increasing functions of adequate upper types. (English) |
| Keyword:
|
integral and derivative operators of functional order |
| Keyword:
|
fractional integral operator |
| Keyword:
|
fractional derivative operator |
| Keyword:
|
spaces of homogeneous type |
| Keyword:
|
Besov spaces |
| Keyword:
|
Triebel-Lizorkin spaces |
| MSC:
|
26A33 |
| MSC:
|
42B35 |
| MSC:
|
46E35 |
| MSC:
|
47G10 |
| idZBL:
|
Zbl 1091.26002 |
| idMR:
|
MR2046192 |
| . |
| Date available:
|
2009-01-08T19:26:34Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119359 |
| . |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[HV] Hartzstein S.I., Viviani B.E.: $T1$ theorems on generalized Besov and Triebel-Lizorkin spaces over spaces of homogeneous type.Revista de la Unión Matemática Argentina 42 1 (2000), 51-73. Zbl 0995.42011, MR 1852730 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| . |
