We obtain characterizations of the pairs of positive measures and for which the discrete non-linear Wolff-type potential associated to sends into .
@article{ASNSP_2009_5_8_2_309_0, author = {Cascante, Carme and Ortega, Joaquin}, title = {On the boundedness of discrete {Wolff} potentials}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {309--331}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 8}, number = {2}, year = {2009}, mrnumber = {2548249}, zbl = {1185.46018}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2009_5_8_2_309_0/} }
TY - JOUR AU - Cascante, Carme AU - Ortega, Joaquin TI - On the boundedness of discrete Wolff potentials JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2009 SP - 309 EP - 331 VL - 8 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2009_5_8_2_309_0/ LA - en ID - ASNSP_2009_5_8_2_309_0 ER -
%0 Journal Article %A Cascante, Carme %A Ortega, Joaquin %T On the boundedness of discrete Wolff potentials %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2009 %P 309-331 %V 8 %N 2 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2009_5_8_2_309_0/ %G en %F ASNSP_2009_5_8_2_309_0
Cascante, Carme; Ortega, Joaquin. On the boundedness of discrete Wolff potentials. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 2, pp. 309-331. http://archive.numdam.org/item/ASNSP_2009_5_8_2_309_0/
[1] “Function Spaces and Potential Theory”, Springer-Verlag, Berlin-Heidelberg-New York, 1996. | MR
and ,[2] Trace inequalities of Sobolev type in the upper triangle case, Proc. London Math. Soc. 80 (2000), 391–414. | MR | Zbl
, and ,[3] Nonlinear potentials and two weight trace inequalities for general dyadic and radial kernels, Indiana Univ. Math. J. 53 (2004), 845–882. | MR | Zbl
, and ,[4] On inequalities, J. London Math. Soc. 7 (2006), 497–511. | MR | Zbl
, and ,[5] Thin sets in nonlinear potential theory, Ann. Inst. Fourier (Grenoble) 33 (1983), 161–187. | EuDML | Numdam | MR | Zbl
and ,[6] The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math. 172 (1994), 137–161. | MR
and ,[7] Potential estimates for a class of fully nonlinear elliptic equations, Duke Math. J. 111 (2002), 1–48. | MR | Zbl
,[8] “Sobolev Spaces”, Springer-Verlag, Berlin-Heidelberg-New York, 1985. | MR
,[9] Quasilinear and Hessian equations of Lane–Emden type, Comm. Partial Differential Equations 31 (2006), 1779–1791. | MR | Zbl
and ,[10] Weighted norm inequalities for operators of potential type and fractional maximal functions, Potential Anal. 5 (1996), 523–580. | MR | Zbl
, and ,[11] Imbedding and multiplier theorems for discrete Littlewood–Paley spaces, Pacific J. Math. 176 (1996), 529–556. | MR | Zbl
,[12] Nonlinear potentials and trace inequalities, Oper. Theory Adv. Appl. 110 (1999), 323–343. | MR | Zbl
,