In this chapter, we establish sharp weighted norm estimates (Buckley-type estimates), generally speaking, for positive kernel operators on spaces of homogeneous type. We discuss the operators involving one-sided maximal and fractional integral operators, Hilbert transforms, multiple integral operators, potential operators, etc. Some of the results are derived via two-weight estimates for integral operators.

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Sharp Bounds in Weighted Inequalities

  • Alexander Meskhi,
  • Humberto Rafeiro,
  • Stefan Samko

摘要

In this chapter, we establish sharp weighted norm estimates (Buckley-type estimates), generally speaking, for positive kernel operators on spaces of homogeneous type. We discuss the operators involving one-sided maximal and fractional integral operators, Hilbert transforms, multiple integral operators, potential operators, etc. Some of the results are derived via two-weight estimates for integral operators.