摘要
In the paper,we study derivative estimates of the iterated spherical averages(At)^(N)(f).We obtain the optimal range of exponents(α,N,p)to ensure the L^(p)boundedness of P(■/■x)(A1)^(N)(f)for 1≤p≤∞,where P is a homogeneous polynomial of degree a.The main theorem extends some known results.As an application,we obtain the smallest N such that(A1)^(N):L^(p)(R^(n))→L_(α)^(p)(R^(n)).
基金
Supported by National Natural Science Foundation of China (Grant Nos. 11771388, 11371316)
the Natural Science Foundation of Zhejiang (Grant No. LQ20A010003)
