Two-weight estimates for strong fractional maximal functions and potentials with multiple kernels

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참고문헌 (46)

1. D. R. Adams, "A trace inequality for generalized potentials", Studia Math, 48, pp.99~105 (1973)
2. Lectures on Lp-potential theory, "D. R. Adams", No.2, ~ (1981)
3. D. R. Adams, "Function Spaces and Potential Theory" (1996), Springer- Verlag
4. J. S. Bradley, "Hardy inequalities with mixed norms", Canad. Math. Bull., 21(4), pp.405~408 (1978)
5. L. Carleson, "An interpolation problem for bounded analytic functions", Amer. J. Math., 80, pp.921~930 (1958)
6. S. Chanillo, "Some integral and maximal operators related to starlike sets", Studia Math, 107(3), pp.223~255 (1993)
7. R. R. Coifman, "Weighted norm inequalities for maximal functions and singular integrals", Studia Math., 51, pp.241~250 (1974)
8. E. M. Dynkin, "Weighted estimates for singular integrals and their applications", Mathematical analysis, 21, pp.42~129 (1983)
9. D. E. Edmunds, "On Fourier multipliers in weighted Triebel-Lizorkin spaces", J. Inequal. Appl., 7(4), pp.555~591 (2002)
10. D. E. Edmunds, "Bounded and Compact Integral Operators", Mathematics and its Applications, 543 (2002), Kluwer Academic Publishers
11. R. Fefferman, "Multiparameter Fourier analysis, Beijing lectures in harmonic analysis", Ann. of Math. Stud., 112, pp.47~130 (1986), Princeton Univ. Press
12. C. Fefferman, "Some maximal inequalities", Amer. J. Math., 93, pp.107~115 (1971)
13. M. Gabidzashvili, "Weighted inequalities for anisotropic potentials", Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR, 82, pp.25~36 (1986)
14. M. Gabidzashvili, "Genebashvili, and V. Kokilashvili, Two-weight inequalities for generalized potentials", translation in Proc. Steklov Inst. Math., 194(4), pp.91~99 (1993)
15. M. Gabidzashvili, "Two weight weak type inequalities for fractional type integrals", Preprint, (45) (1989), Mathematical Institute Czech Acad. Sci.
16. J. Garc´ıa–Cuerva, "Weighted Norm Inequalities and Related Topics", North-Holland Mathematics Studies, 116, pp.104~ (1985), Mathematical Notes, 104, North- Holland Publishing Co.
17. I. Genebashvili, "Weight Theory for Integral Transforms on Spaces of Homogeneous Type", Pitman Monographs and Surveys in Pure and Applied Mathematics, 92 (1998), Longman
18. A. Gogatishvili, "Criteria of strong type two-weighted inequalities for fractional maximal functions", Georgian Math. J., 3(5), pp.423~446 (1996)
19. G. H. Hardy, "Inequalities" (1934), Cambridge Univ. Press
20. L. H¨ormander, "Lp estimates for (pluri-) subharmonic functions", Math. Scand., 20, pp.65~78 (1967)
21. R. Hunt, "Weighted norm inequalities for the conjugate function and Hilbert transform", Trans. Amer. Math. Soc., 176, pp.227~251 (1973)
22. V. M. Kokilashvili, "Weighted Lizorkin-Triebel spaces. Singular integrals, multipliers, imbedding theorems", Trudy Mat. Inst. Steklov., 161, pp.125~149 (1983)
23. V. M. Kokilashvili, "Bisingular integral operators in weighted spaces, Soobshch", Akad. Nauk Gruzin. SSR, 101(2), pp.289~292 (1981)
24. V. M. Kokilashvili, "On Hardy’s inequalities in weighted spaces, Soobshch", Akad. Nauk Gruzin. SSR, 96(1), pp.37~40 (1979)
25. V. Kokilashvili, "Weighted Inequalities in Lorentz and Orlicz Spaces" (1991), World Scientific Publishing Co., Inc.
26. V. Kokilashvili, "On one-sided potentials with multiple kernels", Integral Transforms Spec. Funct., 16(8), pp.669~683 (2005)
27. V. Kokilashvili, "On two-weight estimates for strong fractional maximal functions and potentials with multiple kernels", Proc. A. Razmadze Math. Inst., 137, pp.135~140 (2005)
28. V. Kokilashvili, "On a trace inequality for one-sided potentials with multiple kernels", Fract. Calc. Appl. Anal., 6(4), pp.461~472 (2003)
29. V. Kokilashvili, "Two-weighted criteria for integral transforms with multiple kernels, Approximation and probability", Banach Center Publ., 72, pp.119~140 (2006), Polish Acad. Sci.
30. V. G. Maz’ya, "Sobolev Spaces" (1985), Springer
31. V. G. Maz’ya, "Capacitary inequalities for fractional integrals, with applications to partial differential equations and Sobolev multipliers", Ark. Mat., 33(1), pp.81~115 (1995)
32. A. Meskhi, "A note on two-weight inequalities for multiple Hardy-type operators", J. Funct. Spaces Appl., 3(3), pp.223~237 (2005)
33. B. Muckenhoupt, "Hardy’s inequality with weights", Studia Math., 44, pp.31~38 (1972)
34. B. Muckenhoupt, "Weighted norm inequalities for fractional integrals", Trans. Amer. Math. Soc., 192, pp.261~274 (1974)
35. S. G. Samko, "Fractional Integrals and Derivative, Theory and Applications" (1993), Gordon and Breach Sci. Publishers
36. E. T. Sawyer, "Two weight norm inequalities for certain maximal and integral operators, Harmonic analysis", Lecture Notes in Math., 908, pp.102~127 (1982), Springer
37. E. T. Sawyer, "Weighted norm inequalities for fractional maximal operators, in: Seminar on Harmonic Analysis,Montreal, Que." (1981), CMS Conf. Proc., 1, Amer. Math. Soc.Providence, R.I.
38. E. T. Sawyer, "A two weight weak type inequality for fractional integrals", Trans. Amer. Math. Soc., 281(1), pp.339~345 (1984)
39. E. T. Sawyer, "Multipliers of Besov and power-weighted L2 spaces", Indiana Univ. Math. J., 33(3), pp.353~366 (1984)
40. E. T. Sawyer, "A characterization of two weight norm inequalities for fractional and Poisson integrals", Trans. Amer. Math. Soc., 308(2), pp.533~545 (1988)
41. E. T. Sawyer, "Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces", Amer. J. Math., 114(4), pp.813~874 (1992)
42. E. T. Sawyer, "Weighted norm inequalities for operators of potential type and fractional maximal functions", Potential Anal., 5(6), pp.523~580 (1996)
43. J. O. Str¨omberg, "Weighted Hardy Spaces", Lecture Notes in Math., 1381 (1989), Springer Verlag
44. K. Tachizawa, "On weighted dyadic Carleson’s inequalities", J. Inequal. Appl., 6(4), pp.415~433 (2001)
45. I. E. Verbitsky, "Weighted norm inequalities for integral operators", Trans. Amer. Math. Soc., 350(8), pp.3371~3391 (1998)
46. R. L. Wheeden, "A characterization of some weighted norm inequalities for the fractional maximal function", Studia Math., 107(3), pp.257~272 (1993)