Superlinear equations, potential theory and weighted norm inequalities

Verbitsky, Igor E.

  • Nonlinear Analysis, Function Spaces and Applications, Publisher: Czech Academy of Sciences, Mathematical Institute(Praha), page 223-269

How to cite

top

Verbitsky, Igor E.. "Superlinear equations, potential theory and weighted norm inequalities." Nonlinear Analysis, Function Spaces and Applications. Praha: Czech Academy of Sciences, Mathematical Institute, 1999. 223-269. <http://eudml.org/doc/220702>.

@inProceedings{Verbitsky1999,
author = {Verbitsky, Igor E.},
booktitle = {Nonlinear Analysis, Function Spaces and Applications},
keywords = {Spring school; Proceedings; Nonlinear analysis; Function spaces; Prague (Czech Republic)},
location = {Praha},
pages = {223-269},
publisher = {Czech Academy of Sciences, Mathematical Institute},
title = {Superlinear equations, potential theory and weighted norm inequalities},
url = {http://eudml.org/doc/220702},
year = {1999},
}

TY - CLSWK
AU - Verbitsky, Igor E.
TI - Superlinear equations, potential theory and weighted norm inequalities
T2 - Nonlinear Analysis, Function Spaces and Applications
PY - 1999
CY - Praha
PB - Czech Academy of Sciences, Mathematical Institute
SP - 223
EP - 269
KW - Spring school; Proceedings; Nonlinear analysis; Function spaces; Prague (Czech Republic)
UR - http://eudml.org/doc/220702
ER -

References

top
  1. Adams D. R., Hedberg L. I., Function spaces and potential theory, Springer-Verlag, Berlin 1996. (1996) MR1411441
  2. Adams D. R., Pierre M., Capacitary strong type estimates in semilinear problems, Ann. Inst. Fourier (Grenoble) 41 (1991), 117–135. (1991) Zbl0741.35012MR1112194
  3. Baras P., Semilinear problem with convex nonlinearity, In: Recent Advances in Nonlinear Elliptic and Parabolic Problems. P. Bénilan, M. Chipot, L. C. Evans and M. Pierre (eds.), Pitman Research Notes in Math. Sciences, 208, Longman, Harlow 1989, 202–215. (1989) Zbl0768.35030MR1035008
  4. Baras P., Pierre M., Critère d’existence de solutions positives pour des équations semi-linéaires non monotones, Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985), 185–212. (1985) Zbl0599.35073MR0797270
  5. Bass R. F., Probabilistic techniques in analysis, Springer-Verlag, Berlin 1995. (1995) Zbl0817.60001MR1329542
  6. Birkhoff G., Lattice theory, Amer. Math. Soc., Amer. Math. Soc. Colloq. Publ., 25, Providence, RI 1979. (1979) Zbl0505.06001
  7. Brezis H., Cabre X., Some simple nonlinear PDE’s without solutions, Preprint 1997, 1–37. (1997) MR1638143
  8. Cascante C., Ortega J. M., Verbitsky I. E., On imbedding potential spaces into L q ( d μ ) , To appear in Proc. London Math. Soc. 
  9. Chung K. L., Zhao Z., From Brownian motion to Schrödinger’s equation, Springer-Verlag, Berlin 1995. (1995) Zbl0819.60068MR1329992
  10. Fefferman C., Stein E. M., Some maximal inequalities, Amer. J. Math. 93 (1971) 107–115. (1971) Zbl0222.26019MR0284802
  11. Fefferman R., Strong differentiation with respect to measures, Amer. J. Math. 103 (1981), 33–40. (1981) Zbl0475.42019MR0601461
  12. Frazier M., Jawerth B., A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34–170. (1990) Zbl0716.46031MR1070037
  13. Gurka P., Generalized Hardy’s inequality, Čas. Pěstování Mat. 109 (1984), 194–203. (1984) Zbl0537.26009MR0744875
  14. Hansson K., Imbedding theorems of Sobolev type in potential theory, Math. Scand. 45 (1979), 77–102. (1979) Zbl0437.31009MR0567435
  15. Hansson K., Maz’ya V. G. Verbitsky I. E., Criteria of solvability for multidimensional Riccati’s equations, Ark. Mat. 37 (1999), 87–120. (1999) MR1673427
  16. Hartman P., Ordinary differential equations, Birkhäuser, Boston 1982. (1982) Zbl0476.34002MR0658490
  17. Hedberg L. I., Wolff, Th. H., Thin sets in nonlinear potential theory, Ann. Inst. Fourier (Grenoble) 33 (1983), 161–187. (1983) Zbl0508.31008MR0727526
  18. Hille E., Nonoscillation theorems, Trans. Amer. Math. Soc 64 (1948), 234–252. (1948) MR0027925
  19. Imm, Ch., Semilinear ODEs and Hardy’s inequality with weights, M.S. Thesis, Univ. of Missouri, Columbia 1997, 1–21. (1997) 
  20. Kalton N. J., Verbitsky I. E., Nonlinear equations and weighted norm inequalities, To appear in Trans. Amer. Math. Soc. Zbl0948.35044MR1475688
  21. Kilpeläinen T., Malý J., The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math. 172 (1994), 137–161. (1994) MR1264000
  22. skii M. A. Krasnosel,’ Zabreiko P. P., Geometrical methods of nonlinear analysis, Springer-Verlag, Berlin 1984. (1984) MR0736839
  23. Kufner A., Triebel H., Generalization of Hardy’s inequality, Conf. Semin. Mat. Univ. Bari 156 (1978), 1–21. (1978) MR0541051
  24. Lions P. L., On the existence of positive solutions of semilinear elliptic equations, SIAM Rev. 24 (1982), 441–467. (1982) Zbl0511.35033MR0678562
  25. Malý J., Ziemer W. P., Fine Regularity of solutions of elliptic partial differential equations, Amer. Math. Soc., Providence, RI 1997. (1997) Zbl0882.35001MR1461542
  26. Maz’ya V. G., Classes of domains and embedding theorems for functional spaces, Dokl. Akad. Nauk SSSR, 133 (1960), 527–530. (1960) MR0126152
  27. Maz’ya V. G., On the theory of the n -dimensional Schrödinger operator, Izv. Akad. Nauk SSSR, ser. Mat. 28 (1964), 1145–1172. (1964) MR0174879
  28. Maz’ya V. G., Sobolev Spaces, Springer-Verlag, Berlin 1985. (1985) MR0817985
  29. Maz’ya V. G., Netrusov Y., Some counterexamples for the theory of Sobolev spaces on bad domains, Potential Anal. 4 (1995), 47–65. (1995) Zbl0819.46023MR1313906
  30. Maz’ya V. G., Verbitsky I. E., Capacitary inequalities for fractional integrals, with applications to partial differential equations and Sobolev multipliers, Ark. Mat. 33 (1995), 81–115. (1995) Zbl0834.31006MR1340271
  31. Muckenhoupt B., Hardy’s inequalities with weights, Studia Math. 44 (1972), 31–38. (1972) 
  32. Naïm L., Sur le rôle de la frontière de R. S. Martin dans la théorie du potentiel, Ann. Inst. Fourier (Grenoble) 7 (1957), 183–281. (1957) Zbl0086.30603MR0100174
  33. Nazarov F., Treil S., Volberg A., Bellman functions and two weight inequalities for Haar multipliers, Preprint. Zbl0951.42007MR1685781
  34. Rochberg R., Size estimates for eigenvalues of singular integral operators and Schrödinger operators and for derivatives of quasiconformal mappings, Amer. J. Math. 117 (1995), 711–771. (1995) Zbl0845.42006MR1333943
  35. Sawyer E. T., Weighted norm inequalities for fractional maximal operators, Can. Math. Soc. Conf. Proceedings 1 (1981), 283–309. (1981) Zbl0546.42018MR0670111
  36. Sawyer E. T., A characterization of a two-weight norm inequality for maximal operators, Studia Math. 75 (1982), 1–11 (1982) Zbl0508.42023MR0676801
  37. Sawyer E. T., Two weight norm inequalities for certain maximal and integral operators, Trans. Amer. Math. Soc. 308 (1988), 533–545. (1988) MR0930072
  38. Sawyer E. T., Wheeden R. L., Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), 813–874. (1992) Zbl0783.42011MR1175693
  39. Sawyer E. T., Wheeden R. L., Zhao S., Weighted norm inequalities for operators of potential type and fractional maximal functions, Potential Anal. 5 (1996), 523–580. (1996) Zbl0873.42012MR1437584
  40. Selmi M., Comparaison des noyaux de Green sur les domaines C 1 , 1 , Rev. Roumaine Math. Pures Appl. 36 (1991), 91–100. (1991) MR1144538
  41. Stein E. M., Singular integrals and differentiability properties of functions, Princeton University Press, Princeton 1970. (1970) Zbl0207.13501MR0290095
  42. Tomaselli G., A class of inequalities, Boll. Un. Mat. Ital. 4 (1969), 622–631. (1969) Zbl0188.12103MR0255751
  43. Verbitsky I. E., Weighted norm inequalities for maximal operators and Pisier’s theorem on factorization through L p , , Integral Equations Operator Theory 15 (1992), 121–153. (1992) MR1134691
  44. Verbitsky I. E., Imbedding and multiplier theorems for discrete Littlewood–Paley spaces, Pacific J. Math. 176 (1996), 529-556. (1996) Zbl0865.42009MR1435004
  45. Verbitsky I. E., Wheeden R. L., Weighted inequalities for fractional integrals and applications to semilinear equations, J. Funct. Anal. 129 (1995), 221–241. (1995) MR1322649
  46. Verbitsky I. E., Wheeden R. L., Weighted norm inequalities for integral operators, Trans. Amer. Math. Soc. 350 (1998), 3371–3391. (1998) Zbl0920.42007MR1443202
  47. Widman K.-O., Inequalities for the Green function and boundary continuity of the gradients of solutions of elliptic differential equations, Math. Scand. 21 (1967), 13–67. (1967) MR0239264
  48. Zhao Z., Green function for Schrödinger operator and conditioned Feynman-Kac gauge, J. Math. Anal. Appl. 116 (1986), 309–334. (1986) Zbl0608.35012MR0842803

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.