Integral and derivative operators of functional order on generalized Besov and Triebel-Lizorkin spaces in the setting of spaces of homogeneous type
Hartzstein, Silvia I. ; Viviani, Beatriz E.
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002), p. 723-754 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2002-01-01
Classification:  26A33,  42B35,  46E35,  47G10 
@article{119359,
     author = {Silvia I. Hartzstein and Beatriz E. Viviani},
     title = {Integral and derivative operators of functional order on generalized Besov and Triebel-Lizorkin spaces in the setting of spaces of homogeneous type},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {43},
     year = {2002},
     pages = {723-754},
     zbl = {1091.26002},
     mrnumber = {2046192},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119359}
}

Hartzstein, Silvia I.; Viviani, Beatriz E. Integral and derivative operators of functional order on generalized Besov and Triebel-Lizorkin spaces in the setting of spaces of homogeneous type. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 723-754. http://gdmltest.u-ga.fr/item/119359/

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