A Remark on Certain Integral Operators of Fractional Type

作者：Alejandro Rocha Pablo

来源：Canadian Mathematical Bulletin, 2018, 61(2): 370-375.

DOI：10.4153/CMB-2017-043-6

• integral operator
• Hardy space

For m, n epsilon N, 1 < m <= n, we write n = n(1) + ... + n(m) where {n(1), ... , n(m)} subset of N. Let A(1), ... ,A(m) be n x n singular real matrices such that
circle plus(i=1 1 <= j not equal i <= m) (m) boolean AND N-j = R-n,
where Nj = {x : A(j)x = 0}, dim(N-j) = n - n(j), and A(1)+ ... + A(m) is invertible. In this paper we study integral operators of the form
T(r)f (x) = integral(Rn) vertical bar x - A(1)gamma vertical bar(-n1+alpha 1) ... vertical bar x - A(m)gamma vertical bar(-nm+alpha m) f(y) dy,
n(1) + ... + n(m) = n, alpha(1)/n(1) = ... = alpha(m)/n(m) 0 < r < 1, and the matrices A(i)'s are as above. We obtain the H-P(R-n) - L-q (R-n) boundedness of T-r for 0 < p < 1/r and 1/q = 1/p - r .

• 出版日期2018-6