Boundedness of fractional integral operators on weighted Herz spaces. (Chinese. English summary) Zbl 0981.42011

Long, Shunchao; Wang, Jian

J. Math., Wuhan Univ. 18, No. 3, 349-354 (1998).

Based on atomic decomposition theory, the authors obtain, under some conditions, the boundedness of fractional integral operators from the weighted Herz-type spaces \(\dot K^{\alpha,p}_{q_1}(\omega_1, \omega^{q_1}_2)\) (or \(K^{\alpha,p}_{q_1}(\omega_1, \omega^{q_1}_2)\)) into \(\dot K^{\alpha,p}_{q_2}(\omega_1, \omega^{q_2}_2)\) (or \(K^{\alpha, p}_{q_2}(\omega_1, \omega^{q_2}_2)\)) and from the weighted Herz-type Hardy spaces \(H\dot K^{\alpha, p}_{q_1}(\omega_1, \omega^{q_1}_2)\) (or \(HK^{\alpha, p}_{q_1}(\omega_1, \omega^{q_1}_2)\)) into \(\dot K^{\alpha, p}_{q_2}(\omega_1, \omega^{q_2}_2)\) (or \(K^{\alpha, p}_{q_2}(\omega_1, \omega^{q_2}_2)\)), respectively.

Reviewer: Wang Cun-Zheng (Chengdu)

MSC:

42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
47B38	Linear operators on function spaces (general)
47G10	Integral operators
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Keywords:

boundedness; atomic decomposition; fractional integral operators; weighted Herz-type spaces; weighted Herz-type Hardy spaces