A note on norm inequalities for integral operators on cones
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- by Ke Cheng Zhou PDF
- Trans. Amer. Math. Soc. 347 (1995), 1033-1041 Request permission
Abstract:
Norm inequalities for the Riemann-Liouville operator ${R_r}f(x) = \int _{\langle 0,x\rangle } {\Delta _V^{r - 1}(x - t)f(t)dt}$ and Weyl operator ${W_r}f(x) = \int _{\langle x,\infty \rangle } {\Delta _V^{r - 1}(t - x)f(t)dt}$ on cones in ${R^d}$ have been obtained in the case $r \geqslant 1$ [7]. In this note, these inequalities are further extended to the case $r < 1$. The question of whether the Hardy operator $Hf(x) = \int _{\langle 0,x\rangle } {f(t)dt}$ on cones is bounded from ${L^p}(\Delta _V^\alpha (X))$ to ${L^q}(\Delta _V^\beta (x))\;(q < p)$ is also solved.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 1033-1041
- MSC: Primary 47G10; Secondary 44A15, 46E99
- DOI: https://doi.org/10.1090/S0002-9947-1995-1249897-9
- MathSciNet review: 1249897