JOURNAL BROWSE
Search
Advanced SearchSearch Tips
TWO-WEIGHT ESTIMATES FOR STRONG FRACTIONAL MAXIMAL FUNCTIONS AND POTENTIALS WITH MULTIPLE KERNELS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
TWO-WEIGHT ESTIMATES FOR STRONG FRACTIONAL MAXIMAL FUNCTIONS AND POTENTIALS WITH MULTIPLE KERNELS
Kokilashvili, Vakhtang; Meskhi, Alexander;
  PDF(new window)
 Abstract
In the paper two-weight inequalities of various type for strong fractional maximal functions and potentials with multiple kernels defined on are established.
 Keywords
strong fractional maximal functions;potentials with multiple kernels;two-weight inequality;trace inequality;
 Language
English
 Cited by
1.
Two-Weight Norm Estimates for Multilinear Fractional Integrals in Classical Lebesgue Spaces, Fractional Calculus and Applied Analysis, 2015, 18, 5  crossref(new windwow)
2.
Potential Operators on Cones of Nonincreasing Functions, Journal of Function Spaces and Applications, 2012, 2012, 1  crossref(new windwow)
3.
A characterization of the two-weight inequality for Riesz potentials on cones of radially decreasing functions, Journal of Inequalities and Applications, 2014, 2014, 1, 383  crossref(new windwow)
 References
1.
D. R. Adams, A trace inequality for generalized potentials, Studia Math. 48 (1973), 99–105

2.
D. R. Adams, Lectures on $L^p$-potential theory, Umea Univ. Reports, No.2, 1981

3.
D. R. Adams and L. I. Hedberg, Function Spaces and Potential Theory, Springer-Verlag, Berlin, 1996

4.
J. S. Bradley, Hardy inequalities with mixed norms, Canad. Math. Bull. 21 (1978), no. 4, 405–408

5.
L. Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921–930 crossref(new window)

6.
S. Chanillo, D. K. Watson, and R. L. Wheeden, Some integral and maximal operators related to starlike sets, Studia Math. 107 (1993), no. 3, 223–255

7.
R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250

8.
E. M. Dynkin and B. P. Osilenker, Weighted estimates for singular integrals and their applications,Mathematical analysis, Vol. 21, 42–129, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1983

9.
D. E. Edmunds, V. Kokilashvili, and A. Meskhi, On Fourier multipliers in weighted Triebel-Lizorkin spaces, J. Inequal. Appl. 7 (2002), no. 4, 555–591

10.
D. E. Edmunds, Bounded and Compact Integral Operators, Mathematics and its Applications, Vol. 543, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002

11.
R. Fefferman, Multiparameter Fourier analysis, Beijing lectures in harmonic analysis (Beijing, 1984), 47–130, Ann. of Math. Stud., 112, Princeton Univ. Press, Princeton, NJ, 1986

12.
C. Fefferman and E. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107–115 crossref(new window)

13.
M. Gabidzashvili, Weighted inequalities for anisotropic potentials, Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 82 (1986), 25–36

14.
M. Gabidzashvili, I. Genebashvili, and V. Kokilashvili, Two-weight inequalities for generalized potentials, Trudy Mat. Inst. Steklov. 194 (1992)

15.
Issled. po Teor. Differ. Funktsii Mnogikh Peremen. i ee Prilozh. 14, 89–96; translation in Proc. Steklov Inst. Math. 194 (1993), no. 4, 91–99

16.
M. Gabidzashvili and V. Kokilashvili, Two weight weak type inequalities for fractional type integrals, Preprint, No. 45, Mathematical Institute Czech Acad. Sci., Prague, 1989

17.
J. Garcia–Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Mathematics Studies, 116, Mathematical Notes, 104, North-Holland Publishing Co., Amsterdam, 1985

18.
I. Genebashvili, A. Gogatishvili, V. Kokilashvili, and M. Krbec, Weight Theory for Integral Transforms on Spaces of Homogeneous Type, Pitman Monographs and Surveys in Pure and Applied Mathematics, 92. Longman, Harlow, 1998

19.
A. Gogatishvili and V. Kokilashvili, Criteria of strong type two-weighted inequalities for fractional maximal functions, Georgian Math. J. 3 (1996), no. 5, 423–446 crossref(new window)

20.
G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press, 1934

21.
L. Hormander, L^p$ estimates for (pluri-) subharmonic functions, Math. Scand. 20(1967), 65–78

22.
R. Hunt, B. Muckenhoupt, and R. L. Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227–251 crossref(new window)

23.
V. M. Kokilashvili, Weighted Lizorkin-Triebel spaces. Singular integrals, multipliers, imbedding theorems, Trudy Mat. Inst. Steklov. 161 (1983), 125–149

24.
V. M. Kokilashvili, Bisingular integral operators in weighted spaces, Soobshch. Akad. Nauk Gruzin. SSR 101 (1981), no. 2, 289–292

25.
V. M. Kokilashvili, On Hardy's inequalities in weighted spaces, Soobshch. Akad. Nauk Gruzin. SSR 96 (1979), no. 1, 37–40

26.
V. Kokilashvili and M. Krbec, Weighted Inequalities in Lorentz and Orlicz Spaces,World Scientific Publishing Co., Inc., River Edge, NJ, 1991

27.
V. Kokilashvili and A. Meskhi, On one-sided potentials with multiple kernels, Integral Transforms Spec. Funct. 16 (2005), no. 8, 669–683 crossref(new window)

28.
V. Kokilashvili and A. Meskhi, On two-weight estimates for strong fractional maximal functions and potentials with multiple kernels, Proc. A. Razmadze Math. Inst. 137 (2005), 135–140

29.
V. Kokilashvili and A. Meskhi, On a trace inequality for one-sided potentials with multiple kernels, Fract. Calc. Appl. Anal. 6 (2003), no. 4, 461–472

30.
V. Kokilashvili and A. Meskhi, Two-weighted criteria for integral transforms with multiple kernels, Approximation and probability, 119–140, Banach Center Publ., 72, Polish Acad. Sci., Warsaw, 2006 crossref(new window)

31.
V. G. Maz'ya, Sobolev Spaces, Springer, Berlin, 1985

32.
V. G. Maz'ya and I. E. Verbitsky, Capacitary inequalities for fractional integrals, with applications to partial differential equations and Sobolev multipliers, Ark. Mat. 33 (1995), no. 1, 81–115 crossref(new window)

33.
A. Meskhi, A note on two-weight inequalities for multiple Hardy-type operators, J. Funct. Spaces Appl. 3 (2005), no. 3, 223–237

34.
B. Muckenhoupt, Hardy's inequality with weights, Studia Math. 44 (1972), 31–38

35.
B. Muckenhoupt and R. L. Wheeden, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc. 192 (1974), 261–274 crossref(new window)

36.
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivative, Theory and Applications, Gordon and Breach Sci. Publishers, 1993

37.
E. T. Sawyer, Two weight norm inequalities for certain maximal and integral operators, Harmonic analysis (Minneapolis, Minn., 1981), pp. 102–127, Lecture Notes in Math., 908, Springer, Berlin-New York, 1982 crossref(new window)

38.
E. T. Sawyer, Weighted norm inequalities for fractional maximal operators, in: Seminar on Harmonic Analysis,Montreal, Que., 1980, pp. 283–309, CMS Conf. Proc., 1, Amer. Math. Soc.Providence, R.I., 1981

39.
E. T. Sawyer, A two weight weak type inequality for fractional integrals, Trans. Amer. Math. Soc. 281 (1984), no. 1, 339–345

40.
E. T. Sawyer, Multipliers of Besov and power-weighted $L^2$ spaces, Indiana Univ. Math. J. 33 (1984), no. 3, 353–366

41.
E. T. Sawyer, A characterization of two weight norm inequalities for fractional and Poisson integrals, Trans. Amer. Math. Soc. 308 (1988), no. 2, 533–545

42.
E. T. Sawyer and R. L. Wheeden, Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), no. 4, 813–874

43.
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), no. 6, 523–580

44.
J. O. Stromberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math., Vol. 1381, Springer Verlag, Berlin, 1989

45.
K. Tachizawa, On weighted dyadic Carleson's inequalities, J. Inequal. Appl. 6 (2001), no. 4, 415–433 crossref(new window)

46.
I. E. Verbitsky and R. L. Wheeden, Weighted norm inequalities for integral operators, Trans. Amer. Math. Soc. 350 (1998), no. 8, 3371–3391

47.
R. L. Wheeden, A characterization of some weighted norm inequalities for the fractional maximal function, Studia Math. 107 (1993), no. 3, 257–272