WHICH WEIGHTS ON R ADMIT Lp JACKSON THEOREMS?
نویسنده
چکیده
Let 1 p 1 and W : R ! (0;1) be continuous. Does W admit a Jackson Theorem in Lp? That is, does there exist a sequence f ng 1 n=1 of positive numbers with limit 0 such that inf deg(P ) n k (f P )W kLp(R) n k f W kLp(R) for all absolutely continuous f with k f 0W kLp(R) nite? We show that such a theorem is true i¤ lim x!1 W 1 Lq [0;x] kWkLp[x;1) = 0; where q is the conjugate parameter of p. In an earlier paper, we considered weights admitting a Jackson theorem for all 1 p 1:
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