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 ...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)).展开更多
基金Supported by National Natural Science Foundation of China (Grant Nos. 11771388, 11371316)the Natural Science Foundation of Zhejiang (Grant No. LQ20A010003)
文摘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)).
