Weak type estimates for operators of potential type
Wheeden, Richard ; Zhao, Shiying
Studia Mathematica, Tome 119 (1996), p. 149-160 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:216291 
@article{bwmeta1.element.bwnjournal-article-smv119i2p149bwm,
     author = {Richard Wheeden and Shiying Zhao},
     title = {Weak type estimates for operators of potential type},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {149-160},
     zbl = {0861.42010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv119i2p149bwm}
}

Wheeden, Richard; Zhao, Shiying. Weak type estimates for operators of potential type. Studia Mathematica, Tome 119 (1996) pp. 149-160. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv119i2p149bwm/

[00000] [1] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. | Zbl 0358.30023

[00001] [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. | Zbl 0822.46032

[00002] [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. | Zbl 0803.42011

[00003] [4] E. T. Sawyer, A two weight weak type inequality for fractional integrals, Trans. Amer. Math. Soc. 281 (1984), 339-345. | Zbl 0539.42008

[00004] [5] E. T. Sawyer, A characterization of two weight norm inequalities for fractional and Poisson integrals, ibid. 308 (1988), 533-545. | Zbl 0665.42023

[00005] [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. | Zbl 0783.42011

[00006] [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. | Zbl 0873.42012

[00007] [8] I. E. Verbitsky and R. L. Wheeden, Weighted norm inequalities for integral operators, to appear. | Zbl 0920.42007