Pointwise convergence to initial data of heat and Laplace equations
| Autor: | Beatriz Viviani, Teresa Signes, Silvia Inés Hartzstein, Gustavo Garrigos Aniorte, José Luis Torrea Hernández |
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| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Pointwise convergence
Ornstein-Uhlenbeck Laplace transform Matemáticas Applied Mathematics General Mathematics 010102 general mathematics Mathematical analysis Poisson kernel purl.org/becyt/ford/1.1 [https] Ornstein–Uhlenbeck process 01 natural sciences Hermite Operator Matemática Pura purl.org/becyt/ford/1 [https] 010101 applied mathematics symbols.namesake Weighted Inequalities symbols 0101 mathematics Poisson integral CIENCIAS NATURALES Y EXACTAS Mathematics |
| Zdroj: | CONICET Digital (CONICET) Consejo Nacional de Investigaciones Científicas y Técnicas instacron:CONICET |
| Popis: | Let L be either the Hermite or the Ornstein-Uhlenbeck operator on Rd. We find optimal integrability conditions on a function f for the existence of its heat and Poisson integrals, e−tLf(x) and e−t √Lf(x), solutions respectively of Ut = −LU and Utt = LU on Rd+1 + with initial datum f. As a consequence we identify the most general class of weights v(x) for which such solutions converge a.e. to f for all f ∈ Lp(v), and each p ∈ [1,∞). Moreover, if 1 |
| Databáze: | OpenAIRE |
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