Endpoint Estimates for a Class of Littlewood-Paley Operators with Nondoubling Measures
| Autor: | Qingying Xue, Juyang Zhang |
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| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Journal of Inequalities and Applications, Vol 2009 (2009) |
| Druh dokumentu: | article |
| ISSN: | 1025-5834 1029-242X 72989440 |
| DOI: | 10.1155/2009/175230 |
| Popis: | Let μ be a positive Radon measure on ℝd which may be nondoubling. The only condition that μ satisfies is μ(B(x,r))≤C0rn for all x∈ℝd, r>0, and some fixed constant C0. In this paper, we introduce the operator gλ,μ∗ related to such a measure and assume it is bounded on L2(μ). We then establish its boundedness, respectively, from the Lebesgue space L1(μ) to the weak Lebesgue space L1,∞(μ), from the Hardy space H1(μ) to L1(μ) and from the Lesesgue space L∞(μ) to the space RBLO(μ). As a corollary, we obtain the boundedness of gλ,μ∗ in the Lebesgue space Lp(μ) with p∈(1,∞). |
| Databáze: | Directory of Open Access Journals |
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