no. 2
On the boundedness of discrete Wolff potentials
Cascante, Carme1 ; Ortega, Joaquin1
1 Departament de Matemàtica Aplicada i Anàlisi, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 2, pp. 309-331

We obtain characterizations of the pairs of positive measures μ and ν for which the discrete non-linear Wolff-type potential associated to μ sends L p (dν) into L q (dμ).

Classification : 46E30, 46E35, 31B10

Cascante, Carme 1 ; Ortega, Joaquin 1

1 Departament de Matemàtica Aplicada i Anàlisi, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain 
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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. https://www.numdam.org/item/ASNSP_2009_5_8_2_309_0/

[1] D. R. Adams and L. I. Hedberg, “Function Spaces and Potential Theory”, Springer-Verlag, Berlin-Heidelberg-New York, 1996. | MR

[2] C. Cascante, J. M. Ortega and I. E. Verbitsky, Trace inequalities of Sobolev type in the upper triangle case, Proc. London Math. Soc. 80 (2000), 391–414. | MR | Zbl

[3] C. Cascante, J. M. Ortega and I. E. Verbitsky, Nonlinear potentials and two weight trace inequalities for general dyadic and radial kernels, Indiana Univ. Math. J. 53 (2004), 845–882. | MR | Zbl

[4] C. Cascante, J. M. Ortega and I. E. Verbitsky, On L p -L q inequalities, J. London Math. Soc. 7 (2006), 497–511. | MR | Zbl

[5] L. I. Hedberg and Th. H. Wolff, Thin sets in nonlinear potential theory, Ann. Inst. Fourier (Grenoble) 33 (1983), 161–187. | MR | EuDML | Zbl | Numdam

[6] T. Kilplelaïnen and J. Malýi, The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math. 172 (1994), 137–161. | MR

[7] D. A. Labutin, Potential estimates for a class of fully nonlinear elliptic equations, Duke Math. J. 111 (2002), 1–48. | MR | Zbl

[8] V. G. Maz’Ya, “Sobolev Spaces”, Springer-Verlag, Berlin-Heidelberg-New York, 1985. | MR

[9] N. C. Phuc and I. E. Verbitsky, Quasilinear and Hessian equations of Lane–Emden type, Comm. Partial Differential Equations 31 (2006), 1779–1791. | MR | Zbl

[10] E. T. Sawyer, R. L. Wheeden and S. Zhao, Weighted norm inequalities for operators of potential type and fractional maximal functions, Potential Anal. 5 (1996), 523–580. | MR | Zbl

[11] I. E. Verbitsky, Imbedding and multiplier theorems for discrete Littlewood–Paley spaces, Pacific J. Math. 176 (1996), 529–556. | MR | Zbl

[12] I. E. Verbitsky, Nonlinear potentials and trace inequalities, Oper. Theory Adv. Appl. 110 (1999), 323–343. | MR | Zbl