Endpoint Estimates for a Class of Littlewood-Paley Operators with Nondoubling Measures
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 g&am...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/175230 |
| _version_ | 1811234754190639104 |
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| author | Qingying Xue Juyang Zhang |
| author_facet | Qingying Xue Juyang Zhang |
| author_sort | Qingying Xue |
| collection | DOAJ |
| description | 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,∞). |
| first_indexed | 2024-04-12T11:42:14Z |
| format | Article |
| id | doaj.art-ad81c6e72989440288ab544690fb7146 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-04-12T11:42:14Z |
| publishDate | 2009-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-ad81c6e72989440288ab544690fb71462022-12-22T03:34:36ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2009-01-01200910.1155/2009/175230Endpoint Estimates for a Class of Littlewood-Paley Operators with Nondoubling MeasuresQingying XueJuyang ZhangLet 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,∞).http://dx.doi.org/10.1155/2009/175230 |
| spellingShingle | Qingying Xue Juyang Zhang Endpoint Estimates for a Class of Littlewood-Paley Operators with Nondoubling Measures Journal of Inequalities and Applications |
| title | Endpoint Estimates for a Class of Littlewood-Paley Operators with Nondoubling Measures |
| title_full | Endpoint Estimates for a Class of Littlewood-Paley Operators with Nondoubling Measures |
| title_fullStr | Endpoint Estimates for a Class of Littlewood-Paley Operators with Nondoubling Measures |
| title_full_unstemmed | Endpoint Estimates for a Class of Littlewood-Paley Operators with Nondoubling Measures |
| title_short | Endpoint Estimates for a Class of Littlewood-Paley Operators with Nondoubling Measures |
| title_sort | endpoint estimates for a class of littlewood paley operators with nondoubling measures |
| url | http://dx.doi.org/10.1155/2009/175230 |
| work_keys_str_mv | AT qingyingxue endpointestimatesforaclassoflittlewoodpaleyoperatorswithnondoublingmeasures AT juyangzhang endpointestimatesforaclassoflittlewoodpaleyoperatorswithnondoublingmeasures |