Weighted norm inequalities for integral operators and related topics
Stepanov, Vladimir D.
Nonlinear Analysis, Function Spaces and Applications, GDML_Books, (1994), p. 139-175 / Harvested from
EUDML-ID : urn:eudml:doc:220937
Mots clés:
@article{702462,
     title = {Weighted norm inequalities for integral operators and related topics},
     booktitle = {Nonlinear Analysis, Function Spaces and Applications},
     series = {GDML\_Books},
     publisher = {Prometheus Publishing House},
     address = {Praha},
     year = {1994},
     pages = {139-175},
     mrnumber = {MR1322312},
     zbl = {0866.47025},
     url = {http://dml.mathdoc.fr/item/702462}
}
Stepanov, Vladimir D. Weighted norm inequalities for integral operators and related topics, dans Nonlinear Analysis, Function Spaces and Applications, GDML_Books,  (1994), pp. 139-175. http://gdmltest.u-ga.fr/item/702462/

Bloom, S.; Kerman, R. Weighted LΦ-integral inequalities for operators of Hardy type, Preprint. | MR 1279373

Edmunds, D.E.; Stepanov, V.D. On singular numbers of certain Volterra integral operators, Preprint. | MR 1359927

Korotkov, V.B. Integral operators, Nauka, Novosibirsk, 1983. (Russian) | MR 0721475 | Zbl 1032.45018

Lomakina, E.; Stepanov, V.D. On the compactness and approximation numbers of Hardy type integral operators in Lorentz spaces, Preprint. | MR 1373067 | Zbl 0853.42013

Newman, J.; Solomyak, M. Two-sided estimates on singular values for a class of integral operators on the semi-axes, Preprint. | MR 1299892

Hardy, G.G.; Littlewood, J.E.; Polya, G. Inequalities, Cambridge Univ. Press, 1934. (1934) | Zbl 0010.10703

Lorentz, G.G. On the theory of spaces Λ , Pacific J. Math. 1 (1951), 411–429. (1951) | MR 0044740 | Zbl 0043.11302

Lorentz, G.G. Bernstein polynomials, Univ. of Toronto Press, 1953.. (1953.) | MR 0057370 | Zbl 0051.05001

Krasnosel, M.A. ’sk; Ruticki, Ya.B. Convex functions and Orlicz spaces, Noordhoff, Groningen, 1961. (1961) | MR 0126722

Ando, T. On compactness of integral operators, Indag. Math. (N.S.) 24 (1962), 235–239. (1962) | MR 0139016 | Zbl 0100.11201

Glazman, I.M. Direct methods of qualitative spectral analysis of singular differential operators, Nauka, Moscow, 1963, pp. . (Russian) (1963) | MR 0185471

Aronszajn, N.; Szeptycki, P. On general integral transformations, Math. Ann. 163 (1966), 127–154. (1966) | MR 0190799 | Zbl 0171.12402

Gohberg, I.C.; Krein, M.G. Introduction to the theory of linear non-selfadjoint operators, AMS Transl. Math. Monographs, 18 vol. Providence, R.I., 1969. (1969) | MR 0246142

Talenti, G. Osservazioni sopra una classe di disuguaglianze, Rend. Sem. Mat. Fis. Milano 39 (1969), 171–185. (1969) | MR 0280661 | Zbl 0218.26011

Tomaselli, G. A class of inequalities, Boll. Un. Mat. Ital. (4) 2 (1969), 622–631. (1969) | MR 0255751 | Zbl 0188.12103

Stein, E.M.; Weiss, G. Introduction to Fourier analysis on euclidean spaces, Univ. Press, Princeton, 1971. (1971) | MR 0304972 | Zbl 0232.42007

Muckenhoupt, B. Hardy’s inequality with weights, Studia Math. 44 (1972), 31–38. (1972) | MR 0311856 | Zbl 0236.26015

Riemenschneider, S.D. Compactness of a class of Volterra operators, Tôhoku Math. J. (2) 26 (1974), 385–387. (1974) | MR 0361939 | Zbl 0289.47028

Bergh, J.; Löfström, J. Interpolation spaces: an introduction., Springer Verlag, 1976. (1976) | MR 0482275

Birman, M.Sh.; Solomjak, M.Z. Estimates for the singular numbers of integral operators, Russian Math. Surveys 32 (1977). (1977) | MR 0438186

Schep, A.R. Kernel operators, Thesis, Leiden, 1977. (1977) | MR 0440404

Bradley, J.S. Hardy’s inequalities with mixed normes, Canad. Math. Bull. 21 (1978), 405–408. (1978) | MR 0523580

Kokilashvili, V.M. On Hardy’s inequalities in weighted spaces, Soobshch. Akad. Nauk. Gruzin. SSR 96 (1979), 37–40. (Russian) (1979) | MR 0564755 | Zbl 0434.26007

Simon, B. Trace ideals and their applications, Univ. Press, Cambridge, 1979. (1979) | MR 0541149 | Zbl 0423.47001

Apyshev, O.D.; Otelbaev, M. On the spectrum of a class of differential operators and embedding theorems, Math. USSR-Izv. 15 (1980), 1–24. (1980)

Nikol, N.K. ’ski Lectures on the shift operator, Nauka, Moscow, 1980. (Russian) (1980) | MR 0575166

Andersen, K.; Muckenhoupt, B. Weighted weak type Hardy inequalities with applications to Hilbert transform and maximal functions, Studia Math. 72 (1982), 9–26. (1982) | MR 0665888

Kantorovich, L.V.; Akilov, G.P. Functional Analysis, Pergamon, Oxford, 1982. (1982) | MR 0664597 | Zbl 0484.46003

Sawyer, E.T. Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator, Trans. Amer. Math. Soc. 281 (1984), 329–337. (1984) | MR 0719673 | Zbl 0538.47020

Szeptycki, P. Notes on integral transformations, Dissertationes Math. (Rozprawy Mat.) 231 (1984), 1–52. (1984) | MR 0763933 | Zbl 0558.44001

Maz, V.G. ’y Sobolev spaces, Springer-Verlag, 1985. (1985) | MR 0817985

König, H. Eigenvalue distribution of compact operators, Birkhäuser, Boston, 1986. (1986) | MR 0889455

Edmunds, D.E.; Evans, W.D. Spectral theory and differential operators, Univ. Press, Oxford, 1987. (1987) | MR 0929030 | Zbl 0628.47017

Pietsch, A. Eigenvalues and s-numbers, Geest & Portig, Leipzig, 1987. (1987) | MR 0917067 | Zbl 0615.47019

Edmunds, D.E.; Evans, W.D.; Harris, D.J. Approximation numbers of certain Volterra integral operators, J. London Math. Soc. (2) 37 (1988), 471–489. (1988) | MR 0939123 | Zbl 0658.47049

Stepanov, V.D. Two-weighted estimates for Riemann-Liouville integrals, Report No 39, Math. Inst., Czechoslovak Academy of Sciences, 1988, pp. 28. (1988)

Martín, J.F. -Reye; Sawyer, E. Weighted inequalities for Riemann-Liouville fractional integrals of order one and greater, Proc. Amer. Math. Soc. 106 (1989), 727–733. (1989) | MR 0965246

Stepanov, V.D. Weighted inequalities of Hardy type for higher order derivatives, and their applications, Soviet Math. Dokl. 38 (1989), 389–393. (1989) | MR 0981053 | Zbl 0674.26008

Arino, M.; Muckenhoupt, B. Maximal function on classical Lorentz spaces and Hardy’s inequality with weights for nonincreasing functions, Trans. Amer. Math. Soc. 320 (1990), 727–735. (1990) | MR 0989570

Heinig, H.P. Weighted inequalities in Fourier analysis, Teubner-Texte zur Math. 119, Leipzig, 1990, pp. 42–85. (1990) | MR 1151431 | Zbl 0773.42008

Opic, B.; Kufner, A. Hardy-type Inequalities, Pitman Research Notes in Math. Series 219, Longman Scientific and Technical, Harlow, 1990. (1990) | MR 1069756 | Zbl 0698.26007

Sawyer, E.T. Boundedness of classical operators in classical Lorentz spaces, Studia Math. 96 (1990), 145–158. (1990) | MR 1052631

Stepanov, V.D. Weighted inequalities of Hardy type for higher order derivatives, Proc. Steklov Inst. Math. 187 (1990), no. 3, 205–220. (1990)

Stepanov, V.D. Weighted inequalities of Hardy type for Riemann-Liouville fractional integrals, Siberian Math. J. 31 (1990), 513–522. (1990) | MR 1084772

Stepanov, V.D. On the boundedness and compactness of a class of integral operators, Soviet Math. Dokl. 41 (1990), 468–470. (1990) | MR 1071870

Andersen, K. Weighted generalized Hardy inequalities for nonincreasing functions, Canad. J. Math. 43 (1991), 1121–1135. (1991) | MR 1145581 | Zbl 0757.26018

Bloom, S.; Kerman, R. Weighted norm inequalities for operators of Hardy type, Proc. Amer. Math. Soc. 113 (1991), 135–141. (1991) | MR 1059623 | Zbl 0753.42010

Hernandez, E. Weighted inequalities through factorization, Publ. Mat. 35 (1991), 141–153. (1991) | MR 1103612 | Zbl 0722.42012

Neugebauer, C.J. Weighted norm inequalities for averaging operators on monotone functions, Publ. Mat. 35 (1991), 429–447. (1991) | MR 1201565

Sinnamon, G. Weighted Hardy and Opial type inequalities, J. Math. Anal. Appl. 160 (1991), 433–445. (1991) | MR 1126128 | Zbl 0756.26011

Stepanov, V.D. Two-weighted estimates of Riemann-Liouville integrals, Math. USSR-Izv. 36 (1991), 669–681. (1991) | MR 1072699 | Zbl 0724.26011

Stepanov, V.D. Integral operators on the cone of monotone functions and embeddings of Lorentz spaces, Soviet Math. Dokl. 43 (1991), 620–623. (1991) | MR 1118029

Gol, M.L. ’dma Function spaces and their applications, Patrice Lumumba Univ., 1991, pp. 35–67. (1991, pp. 35–67)

Gol, M.L. ’dma On integral inequalities on a cone of functions with monotonicity properties, Soviet Math. Dokl. 42 (1992), 581–587. (1992) | MR 1152406

Heinig, H.P.; Maligranda, L. Interpolation with weights in Orlicz spaces, Department of Applied Mathematics, Lulea University of Technology, 1992, Research Report 03. (1992)

Oinarov, R. Weighted inequalities for a class of integral operators, Soviet Math. Dokl. 44 (1992), 291–293. (1992) | MR 1152890

Stepanov, V.D. Weighted inequalities for a class of Volterra convolution operators, J. London Math. Soc. (2) 45 (1992), 232–242. (1992) | MR 1171551 | Zbl 0703.42011

Braverman, M.Sh. On a class of operators, J. London Math. Soc. (2) 47 (1993), 119–128. (1993) | MR 1200982 | Zbl 0732.47033

Carro, M.J.; Soria, J. Weighted Lorentz spaces and the Hardy operator, J. Funct. Anal. 112 (1993), 480–494. (1993) | MR 1213148 | Zbl 0784.46022

Carro, M.J.; Soria, J. Boundedness of some integral operators, Canad. J. Math. 45 (1993), 1155–1166. (1993) | MR 1247539 | Zbl 0798.42010

Gol, M.L. ’dma On integral inequalities on the set of functions with some properties of monotonicity, Function Spaces, Differential Operators and Nonlinear Analysis, Teubner Texte zur Math. 133, Leipzig, 1993, pp. 274–279. (1993) | MR 1242589

Heinig, H.P.; Stepanov, V.D. Weighted Hardy inequalities for increasing functions, Canad. J. Math. 45 (1993), 104–116. (1993) | MR 1200323 | Zbl 0796.26008

Myasnikov, E.A.; Persson, L.E.; Stepanov, V.D. On the best constants in certain integral inequalities for monotone functions, Lulea University of Technology, Department of Mathematics, 1993, Research Report 15. (1993) | MR 1317179

Nowak, K. Schatten ideal behaviour of a generalized Hardy operator, Proc. Amer. Math. Soc. 118 (1993), 479–483. (1993) | MR 1152990

Oinarov, R. Two-sides estimates of a certain classes of integral operators, Proc. Steklov Inst. Math. 204 (1993), 240–250. (Russian) (1993) | MR 1320028

Sinnamon, G. Spaces defined by level functions and their duals, Preprint, 1993, pp. 30. (1993) | MR 1292851

Stepanov, V.D. The weighted Hardy’s inequality for nonincreasing functions, Trans. Amer. Math. Soc. 338 (1993), 173–186. (1993) | MR 1097171 | Zbl 0786.26015

Stepanov, V.D. On weighted estimates for a class of integral operators, Siberian Math. J. 34 (1993), 755–766. (1993) | MR 1248804 | Zbl 0815.47064

Stepanov, V.D. Integral operators on the cone of monotone functions, J. London Math. Soc. (2) 48 (1993), 465–487. (1993) | MR 1241782 | Zbl 0837.26011

Braverman, M.Sh.; Stepanov, V.D. On the discrete Hardy inequality, Bull. London Math. Soc. (1994), to appear. (1994) | MR 1289048 | Zbl 0806.26011

Edmunds, D.E.; Gurka, P.; Pick, L. Compactness of Hardy type integral operators in weighted Banach function spaces, Studia Math. 109 (1994), 73–90. (1994) | MR 1267713 | Zbl 0821.46036

Edmunds, D.E.; Stepanov, V.D. The measure of non-compactness and approximation numbers of certain Volterra integral operators, Math. Ann. 298 (1994), 41–66. (1994) | MR 1252816 | Zbl 0788.45013

Gol, M.L. ’dma; Heinig, H.P.; Stepanov, V.D. On the principle of duality in the Lorentz spaces, Russian Acad. Sci. Dokl. Math. (1994), to appear. (Russian) (1994) | MR 1414066

Lai, Qinsheng Weighted integral inequalities for the Hardy type operator and the fractional maximal operator, J. London Math. Soc. (2) 49 (1994), 244–266. (1994) | MR 1260111 | Zbl 0794.42015

Sinnamon, G.; Stepanov, V.D. The weighted Hardy inequality: new proofs and the case p=1 , Preprint, 1994, pp. 15. (1994) | MR 1395069

Stepanov, V.D. Weighted norm inequalities of Hardy type for a class of integral operators, J. London Math. Soc. (1994), to appear. (1994) | MR 1277757 | Zbl 0837.26012

Stepanov, V.D. On singular numbers of certain class of integral operators, Russian Acad. Sci. Dokl. Math. 336 (1994), 457–458. (Russian) (1994) | MR 1289518