Abstract
In this paper, we study integral operators of the form
, where A i are certain invertible matrices, α i > 0, 1 ≤ i ≤ m, α 1 + … + α m = n − α, 0 ≤ α < n. For \(\tfrac{1} {q} = \tfrac{1} {p} - \tfrac{\alpha } {n}\), we obtain the L p(ℝn, w p) − L q(ℝn,w q) boundedness for weights w in A(p, q) satisfying that there exists c > 0 such that w(A i x) ≤ cw(x), a.e. x ∈ ℝn, 1 ≤ i ≤ m. Moreover, we obtain the appropriate weighted BMO and weak type estimates for certain weights satisfying the above inequality. We also give a Coifman type estimate for these operators.
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Riveros, M.S., Urciuolo, M. Weighted inequalities for fractional type operators with some homogeneous kernels. Acta. Math. Sin.-English Ser. 29, 449–460 (2013). https://doi.org/10.1007/s10114-013-1639-9
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DOI: https://doi.org/10.1007/s10114-013-1639-9