Weak type estimates for operators of potential type

Richard Wheeden; Shiying Zhao

Studia Mathematica (1996)

  • Volume: 119, Issue: 2, page 149-160
  • ISSN: 0039-3223

Abstract

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We derive two-weight weak type estimates for operators of potential type in homogeneous spaces. The conditions imposed on the weights are testing conditions of the kind first studied by E. T. Sawyer [4]. We also give some applications to strong type estimates as well as to operators on half-spaces.

How to cite

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Wheeden, Richard, and Zhao, Shiying. "Weak type estimates for operators of potential type." Studia Mathematica 119.2 (1996): 149-160. <http://eudml.org/doc/216291>.

@article{Wheeden1996,
abstract = {We derive two-weight weak type estimates for operators of potential type in homogeneous spaces. The conditions imposed on the weights are testing conditions of the kind first studied by E. T. Sawyer [4]. We also give some applications to strong type estimates as well as to operators on half-spaces.},
author = {Wheeden, Richard, Zhao, Shiying},
journal = {Studia Mathematica},
keywords = {norm inequality; weight; operator of potential type; homogeneous space; weak type inequalities; potential type operator; strong type inequalities},
language = {eng},
number = {2},
pages = {149-160},
title = {Weak type estimates for operators of potential type},
url = {http://eudml.org/doc/216291},
volume = {119},
year = {1996},
}

TY - JOUR
AU - Wheeden, Richard
AU - Zhao, Shiying
TI - Weak type estimates for operators of potential type
JO - Studia Mathematica
PY - 1996
VL - 119
IS - 2
SP - 149
EP - 160
AB - We derive two-weight weak type estimates for operators of potential type in homogeneous spaces. The conditions imposed on the weights are testing conditions of the kind first studied by E. T. Sawyer [4]. We also give some applications to strong type estimates as well as to operators on half-spaces.
LA - eng
KW - norm inequality; weight; operator of potential type; homogeneous space; weak type inequalities; potential type operator; strong type inequalities
UR - http://eudml.org/doc/216291
ER -

References

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  1. [1] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. Zbl0358.30023
  2. [2] B. Franchi, C. E. Gutierrez and R. L. Wheeden, Weighted Sobolev-Poincaré inequalities for Grushin type operators, Comm. Partial Differential Equations 19 (1994), 523-604. Zbl0822.46032
  3. [3] I. Genebashvili, A. Gogatishvili and V. Kokilashvili, Criteria of general weak type inequalities for integral transforms with positive kernels, Proc. Georgian Acad. Sci. Math. 1 (1993), 11-34. Zbl0803.42011
  4. [4] E. T. Sawyer, A two weight weak type inequality for fractional integrals, Trans. Amer. Math. Soc. 281 (1984), 339-345. Zbl0539.42008
  5. [5] E. T. Sawyer, A characterization of two weight norm inequalities for fractional and Poisson integrals, ibid. 308 (1988), 533-545. Zbl0665.42023
  6. [6] E. T. Sawyer and R. L. Wheeden, Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), 813-874. Zbl0783.42011
  7. [7] E. T. Sawyer, R. L. Wheeden and S. Zhao, Weighted norm inequalities for operators of potential type and fractional maximal functions, Potential Anal. (1996), to appear. Zbl0873.42012
  8. [8] I. E. Verbitsky and R. L. Wheeden, Weighted norm inequalities for integral operators, to appear. Zbl0920.42007

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