Pointwise Convergence of Fejer Type Means
نویسندگان
چکیده
Let P be a compact n-dimensional convex polyhedron in R n containing the origin in its interior and let e H(t) = Z 1 0 Z vP e 2it ddv, t2 R n ;where vP is the characteristic function of the dilated polyhedron vP. Let H N (t) = X m2Z n e H 1 N+1 (t+m), t 2 T n , where e H " (t) = " ?n e H(t="). We prove that (e H " f)(t) ! f(t) a.e., as " ! 0, for any f 2 L 1 (R n), and that (H N f)(t) ! f(t) a.e., as N ! 1, for any f 2 L 1 (T n).
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