References
- D. R. Adams, A trace inequality for generalized potentials, Studia Math. 48 (1973), 99–105
-
D. R. Adams, Lectures on
$L^p$ -potential theory, Umea Univ. Reports, No.2, 1981 - D. R. Adams and L. I. Hedberg, Function Spaces and Potential Theory, Springer-Verlag, Berlin, 1996
- J. S. Bradley, Hardy inequalities with mixed norms, Canad. Math. Bull. 21 (1978), no. 4, 405–408
- L. Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921–930 https://doi.org/10.2307/2372840
- 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
- R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250
- 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
- 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
- D. E. Edmunds, Bounded and Compact Integral Operators, Mathematics and its Applications, Vol. 543, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002
- 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
- C. Fefferman and E. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107–115 https://doi.org/10.2307/2373450
- M. Gabidzashvili, Weighted inequalities for anisotropic potentials, Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 82 (1986), 25–36
- M. Gabidzashvili, I. Genebashvili, and V. Kokilashvili, Two-weight inequalities for generalized potentials, Trudy Mat. Inst. Steklov. 194 (1992)
- 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
- M. Gabidzashvili and V. Kokilashvili, Two weight weak type inequalities for fractional type integrals, Preprint, No. 45, Mathematical Institute Czech Acad. Sci., Prague, 1989
- 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
- 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
- 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 https://doi.org/10.1007/BF02259772
- G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press, 1934
-
L. Hormander,
L^p$ estimates for (pluri-) subharmonic functions, Math. Scand. 20(1967), 65–78 - 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 https://doi.org/10.2307/1996205
- V. M. Kokilashvili, Weighted Lizorkin-Triebel spaces. Singular integrals, multipliers, imbedding theorems, Trudy Mat. Inst. Steklov. 161 (1983), 125–149
- V. M. Kokilashvili, Bisingular integral operators in weighted spaces, Soobshch. Akad. Nauk Gruzin. SSR 101 (1981), no. 2, 289–292
- V. M. Kokilashvili, On Hardy's inequalities in weighted spaces, Soobshch. Akad. Nauk Gruzin. SSR 96 (1979), no. 1, 37–40
- V. Kokilashvili and M. Krbec, Weighted Inequalities in Lorentz and Orlicz Spaces,World Scientific Publishing Co., Inc., River Edge, NJ, 1991
- V. Kokilashvili and A. Meskhi, On one-sided potentials with multiple kernels, Integral Transforms Spec. Funct. 16 (2005), no. 8, 669–683 https://doi.org/10.1080/10652460500106105
- 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
- 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
- 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 https://doi.org/10.4064/bc72-0-9
- V. G. Maz'ya, Sobolev Spaces, Springer, Berlin, 1985
- 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 https://doi.org/10.1007/BF02559606
- A. Meskhi, A note on two-weight inequalities for multiple Hardy-type operators, J. Funct. Spaces Appl. 3 (2005), no. 3, 223–237
- B. Muckenhoupt, Hardy's inequality with weights, Studia Math. 44 (1972), 31–38
- B. Muckenhoupt and R. L. Wheeden, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc. 192 (1974), 261–274 https://doi.org/10.2307/1996833
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivative, Theory and Applications, Gordon and Breach Sci. Publishers, 1993
- 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 https://doi.org/10.1007/BFb0093283
- 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
- E. T. Sawyer, A two weight weak type inequality for fractional integrals, Trans. Amer. Math. Soc. 281 (1984), no. 1, 339–345
-
E. T. Sawyer, Multipliers of Besov and power-weighted
$L^2$ spaces, Indiana Univ. Math. J. 33 (1984), no. 3, 353–366 - 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
- 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
- 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
- J. O. Stromberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math., Vol. 1381, Springer Verlag, Berlin, 1989
- K. Tachizawa, On weighted dyadic Carleson's inequalities, J. Inequal. Appl. 6 (2001), no. 4, 415–433 https://doi.org/10.1155/S102558340100025X
- I. E. Verbitsky and R. L. Wheeden, Weighted norm inequalities for integral operators, Trans. Amer. Math. Soc. 350 (1998), no. 8, 3371–3391
- R. L. Wheeden, A characterization of some weighted norm inequalities for the fractional maximal function, Studia Math. 107 (1993), no. 3, 257–272
Cited by
- Two-Weight Norm Estimates for Multilinear Fractional Integrals in Classical Lebesgue Spaces vol.18, pp.5, 2015, https://doi.org/10.1515/fca-2015-0066
- Potential Operators on Cones of Nonincreasing Functions vol.2012, 2012, https://doi.org/10.1155/2012/474681
- A characterization of the two-weight inequality for Riesz potentials on cones of radially decreasing functions vol.2014, pp.1, 2014, https://doi.org/10.1186/1029-242X-2014-383
- The Fefferman–Stein Type Inequalities for Strong Fractional Maximal Operators vol.74, pp.1, 2019, https://doi.org/10.1007/s00025-018-0927-1
- Off-diagonal extrapolation on mixed variable Lebesgue spaces and its applications to strong fractional maximal operators vol.0, pp.0, 2018, https://doi.org/10.1515/gmj-2018-0073