Local maximal functions and operators associated to Laguerre expansions
In this paper we get sharp conditions on a weight v which allow us to obtain some weighted inequalities for a local Hardy-Littlewood Maximal operator defined on an open set in the Euclidean n-space. This result is applied to assure a pointwise convergence of the Laguerre heat-diffusion semigroup u(x...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2014 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/100579 |
| Online Access: | http://hdl.handle.net/11336/100579 |
| Access Level: | Open access |
| Keyword: | HEAT DIFFUSION SEMIGROUP LAGUERRE LAGUERRE-RIESZ TRANSFORMS LOCAL MAXIMAL OPERATOR WEIGHTS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | In this paper we get sharp conditions on a weight v which allow us to obtain some weighted inequalities for a local Hardy-Littlewood Maximal operator defined on an open set in the Euclidean n-space. This result is applied to assure a pointwise convergence of the Laguerre heat-diffusion semigroup u(x,t) = (T(t)f)(x) to f when t tends to zero for all functions f in L p(v(x)dx) for p greater than or equal to 1 and a weight v. In proving this we obtain weighted inequalities for the maximal operator associated to the Laguerre diffusion semigroup of the Laguerre differential operator of order greater than or equal to 0. Finally, as a by-product, we obtain weighted inequalities for the Riesz-Laguerre operators. |
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