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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2016.1
- 수록면
- 185 - 220 (36page)
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We study the Gauss and Poisson semigroups connected with the Riemann-Liouville operator defined on the half plane. Next, we establish aprinciple of maximum for the singular partial differential operator$$\Delta_\alpha=\frac{\partial^2}{\partial r^2}+\frac{2\alpha+1}{r}\ \frac{\partial}{\partial r}+\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial t^2};\(r,x,t)\in\ ]0,+\infty[\times\mathbb{R}\times]0,+\infty[.$$Later, we define the Littlewood-Paley $g$-function and using the principle of maximum, we prove that for every $p\in\ ]1,+\infty[$, there exists a positive constant$C_p$ such that for every $f\in\ L^p(d\nu_\alpha)$,$$\frac{1}{C_p}\ ||f||_{p,\nu_\alpha}\leqslant ||g(f)||_{p,\nu_\alpha}\leqslant C_p\ ||f||_{p,\nu_\alpha}.$$
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참고문헌 (30)
참고문헌 신청
A. Achour / 1983 / La g-fonction de Littlewood-Paley associee µa un operateur differentiel singulier sur ]0;+∞[ / Ann. Inst. Fourier, Grenoble 33:203~226
B. Amri / 2013 / The Littlewood-Paley g-function associated with the Riemann-Liouville operator / Ann. Univ. Paedagog. Crac. Stud. Math. 12:31~58
B. Amri / Uncertainty principle in terms of entropy for the Riemann-Liouville operator / Bull. Malays. Math. Sci. Soc
B. Amri / 2013 / Beckner Logarithmic Uncertainty principle for the Riemann-Liouville operator / Internat. J. Math. 24(9):1350070
B. Amri / 2014 / Calderon-reproducing formula for singular partial differ-ential operators / Integral Transforms Spec. Funct. 25(8):597~611
B. Amri / 2013 / The Littlewood-Paley g-function associated with the Riemann-Liouville operator / Ann. Univ. Paedagog. Crac. Stud. Math. 12:31~58
B. Amri / Uncertainty principle in terms of entropy for the Riemann-Liouville operator / Bull. Malays. Math. Sci. Soc
B. Amri / 2013 / Beckner Logarithmic Uncertainty principle for the Riemann-Liouville operator / Internat. J. Math. 24(9):1350070
B. Amri / 2014 / Calderon-reproducing formula for singular partial differ-ential operators / Integral Transforms Spec. Funct. 25(8):597~611
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