Fatou type weighted pointwise convergence of nonlinear singular integral operators Depending on two parameters
In this paper we present some theorems concerning existence and Fatou type weighted pointwise convergence of nonlinear singular integral operators of the form: (Tλf)(x)=∫RKλ(t−x; f(t))dt, x∈R, λ∈Λ$({T_\lambda }f)(x) = \int\limits_R {{K_\lambda }} (t - x;{\rm{ }}f(t))dt,{\rm{ x}} \in R,{\rm{ }}\lamb...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2016-01-01
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| Series: | MATEC Web of Conferences |
| Online Access: | http://dx.doi.org/10.1051/matecconf/20166816002 |
| Summary: | In this paper we present some theorems concerning existence and Fatou type weighted pointwise convergence of nonlinear singular integral operators of the form:
(Tλf)(x)=∫RKλ(t−x; f(t))dt, x∈R, λ∈Λ$({T_\lambda }f)(x) = \int\limits_R {{K_\lambda }} (t - x;{\rm{ }}f(t))dt,{\rm{ x}} \in R,{\rm{ }}\lambda \in \Lambda $ where Λ ≠ ∅ is a set of non-negative indices, at a common generalized Lebesgue point of the functions f ∈ L1,ϕ (R) and positive weight function φ. Here, L1,ϕ (R) is the space of all measurable functions for which |fϕ|$\left| {{f \over \phi }} \right|$ is integrable on R. |
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| ISSN: | 2261-236X |