| Title:
|
Weights, one-sided operators, singular integrals and ergodic theorems (English) |
| Author:
|
Martín-Reyes, Francisco Javier |
| Language:
|
English |
| Journal:
|
Nonlinear Analysis, Function Spaces and Applications |
| Volume:
|
Vol. 5 |
| Issue:
|
1994 |
| Year:
|
|
| Pages:
|
103-137 |
| . |
| Category:
|
math |
| . |
| MSC:
|
28D05 |
| MSC:
|
42B20 |
| MSC:
|
46E30 |
| MSC:
|
47B38 |
| MSC:
|
47G10 |
| idZBL:
|
Zbl 0870.47021 |
| idMR:
|
MR1322311 |
| . |
| Date available:
|
2009-10-08T09:45:08Z |
| Last updated:
|
2012-08-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/702453 |
| . |
| Reference:
|
[A] Akcoglu, M.A.: A pointwise ergodic theorem in $L_p$-spaces.Canad. J. Math. 27 (1975), 1075-1082. Zbl 0326.47005, MR 0396901 |
| Reference:
|
[AFM] Aimar, H., Forzani, L., Martín, F.J. -Reye: On weighted inequalities for one-sided singular integrals.preprint. |
| Reference:
|
[An] Andersen, K.F.: Weighted inequalities for maximal functions associated with general measures.Trans. Amer. Math. Soc. 326 (1991), 907–920. Zbl 0736.42013, MR 1038012 |
| Reference:
|
[AM] Andersen, K. F., Muckenhoupt, B.: Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions.Studia Math. 72 (1982), 9–26. Zbl 0501.47011, MR 0665888 |
| Reference:
|
[AS] Andersen, K.F., Sawyer, E.T.: Weighted norm inequalities for the Riemann-Liouville and Weyl fractional integral operators.Trans. Amer. Math. Soc. 308 (1988), 547–557. Zbl 0664.26002, MR 0930071 |
| Reference:
|
[B] Birkhoff, G. D.: Proof of the ergodic theorem.Proc. Nat. Acad. Sci. U.S.A. 17 (1931), 656–660. Zbl 0003.25602 |
| Reference:
|
[Br] Bradley, S.: Hardy inequalities with mixed norms.Canad. Math. Bull. (1978), 405–408. Zbl 0402.26006, MR 0523580 |
| Reference:
|
[Bru] Brunel, A.: Théorème ergodique pour les opérateurs positifs à moyennes bornées sur les espaces $L_p$ $(1<p<\infty )$.Ergodic Theory Dynamical Systems 12 (1993), 195-207. MR 1176617 |
| Reference:
|
[BE] Brunel, A., Emilion, R.: Sur les opérateurs positifs à moyennes bornées.C. R. Acad. Sci. Paris I 298 (1984), 103–106. Zbl 0582.47038, MR 0741070 |
| Reference:
|
[CF] Coifman, R., Fefferman, C.: Weighted norm inequalities for maximal functions and singular integrals.Studia Math. 51 (1974), 241–250. Zbl 0291.44007, MR 0358205 |
| Reference:
|
[CJR] Coifman, R., Jones, P., Francia, J. L. Rubio de: Constructive decomposition of $B.M.O.$ functions and factorization of $A_p$ weights.Proc. Amer. Math. Soc. 87 (1983), 675–676. MR 0687639 |
| Reference:
|
[DS] Dunford, N., Schwartz, J. T.: Convergence almost everywhere of operator averages.J. Rat. Mech. Anal. 5 (1956), 129–178. Zbl 0075.12102, MR 0077090 |
| Reference:
|
[FMT] Cabrera, L.M. Fernández, Martín, F.J. -Reye, Torrea, J. L.: On the ergodic averages and the ergodic Hilbert transform.preprint. |
| Reference:
|
[G] Gallardo, D.: Weighted integral inqualities for the ergodic maximal operator and other sublinear operators. Convergence of the averages and the ergodic Hilbert transform.Studia Math. 94 (1989), 121–147. MR 1025742 |
| Reference:
|
[GM] Gallardo, D., Martín, F.J. -Reye: On the almost everywhere existence of the ergodic Hilbert transform.Proc. Amer. Math. Soc. 105 (1989), 636–643. MR 0939964 |
| Reference:
|
[GR] García, J. -Cuerv, Francia, J. L. Rubio de: Weighted norm inequalities and related topics.North-Holland, 1985. MR 0807149 |
| Reference:
|
[HMW] Hunt, R.A., Muckenhoupt, B., Wheeden, R.L.: Weighted norm inequalities for the conjugate function and the Hilbert transform.Trans. Amer. Math. Soc. 176 (1973), 261–274. MR 0312139 |
| Reference:
|
[I ] Ionescu, A. -Tulce: Ergodic properties of isometries in $L^p$-spaces, $1<p<\infty $.Bull. Amer. Math. Soc. 70 (1964), 366-371. MR 0206207 |
| Reference:
|
[JT] Jurkat, W., Troutman, J.: Maximal inequalities related to generalized a.e. continuity.Trans. Amer. Math. Soc. 252 (1979), 49–64. Zbl 0441.42023, MR 0534110 |
| Reference:
|
[K ] Kan, Charn-Huen: Ergodic properties for Lamperti operators.Canad. J. Math. 30 (1978), 1206–1214. MR 0511557 |
| Reference:
|
[Kr] Krengel, U.: Ergodic theorems.Walter de Gruyter, 1985. Zbl 0575.28009, MR 0797411 |
| Reference:
|
[KG] Kokilashvili, V., Gabidzashvili, M.: Two weight weak type inequalities for fractional type integrals..Preprint Math. Inst. Czech. Acad. Sci. Prague 45 (1989). |
| Reference:
|
[LT] Lorente, M., Torre, A. de la: Weighted inequalities for some one-sided operators.preprint. Zbl 0895.26002 |
| Reference:
|
[M] Martín, F.J. -Reye: New proofs of weighted inequalities for the one sided Hardy-Littlewood maximal functions.Proc. Amer. Math. Soc. 117 (1993), 691–698. MR 1111435 |
| Reference:
|
[MO] Martín, F.J. -Reye, Salvador, P. Ortega: Ergodic power functions for mean bounded, invertible, positive operators.Studia Math. 91 (1988), 131–139. MR 0985080 |
| Reference:
|
[MOT] Martín, F.J. -Reye, Salvador, P. Ortega, Torre, A. de la: Weighted inequalities for one-sided maximal functions.Trans. Amer. Math. Soc. 319 (1990), 517–534. MR 0986694 |
| Reference:
|
[MPT] Martín, F.J. -Reye, Pick, L., Torre, A. de la: $A_\infty ^+$ condition.Canad. J. Math. 45 (1993), 1231–1244. MR 1247544 |
| Reference:
|
[MT1] Martín, F.J. -Reye, Torre, A. de la: The dominated ergodic estimate for mean bounded, invertible, positive operators.Proc. Amer. Math. Soc. 104 (1988), 69–75. MR 0958045 |
| Reference:
|
[MT2] Martín, F.J. -Reye, Torre, A. de la: On the almost everywhere convergence of the ergodic averages.Ergodic Theory Dynamical Systems 10 (1990), 141–149. MR 1053804 |
| Reference:
|
[MT3] Martín, F.J. -Reye, Torre, A. de la: Two weight norm inequalities for fractional one-sided maximal operators.Proc. Amer. Math. Soc. 117 (1993), 483–489. MR 1110548 |
| Reference:
|
[MT4] Martín, F.J. -Reye, Torre, A. de la: One-sided BMO spaces.J. London Math. Soc. 49 (1994), 529–542. MR 1271548 |
| Reference:
|
[MT5] Martín, F.J. -Reye, Torre, A. de la: Weights for general one-sided maximal operators.preprint. |
| Reference:
|
[Mu] Muckenhoupt, B.: Weighted norm inequalities for the Hardy maximal function.Trans. Amer. Math. Soc. 165 (1972), 207–226.. Zbl 0236.26016, MR 0293384 |
| Reference:
|
[OK] Opic, B., Kufner, A.: Hardy-type inequalities.Longman Scientific and Technical, 1990. Zbl 0698.26007, MR 1069756 |
| Reference:
|
[O1] Ortega, P.: Pesos para operadores maximales y teoremas ergódicos en espacios $L_p$, $L_{p,q}$ y de Orlicz.Thesis, Universidad de Málaga, 1991. |
| Reference:
|
[O2] Ortega, P.: Convergence of the averages and finiteness of ergodic power functions in weighted $L^1$ spaces.Publ. Mat. 35 (1991), 465–473. MR 1201568 |
| Reference:
|
[O3] Ortega, P.: Weights for the ergodic maximal operator and a.e. convergence of the ergodic averages for functions in Lorentz spaces.Tôhoku Math. J. 45 (1993), 437–446. MR 1231566 |
| Reference:
|
[O4] Ortega, P.: Weighted Lorentz norm inequalities for the one-sided Hardy-Littlewood maximal functions and for the maximal ergodic operator.to appear in Canad. J. Math. MR 1295131 |
| Reference:
|
[O5] Ortega, P.: Weighted inequalities for the one-sided maximal functions in Orlicz spaces.to appear in Studia Math.. MR 1636403 |
| Reference:
|
[OP] Salvador, P. Ortega, Pick, L.: Two weight weak and extra-weak type inequalities for the one-sided maximal operator.Proc. Roy. Soc. Edinburgh Sect. A (1993), 1109–1118. Zbl 0806.42011, MR 1263909 |
| Reference:
|
[R] Francia, J. L. Rubio de: Factorization theory and $A_p$ weights.Amer. J. Math. 106 (1984), 533–546. MR 0745140 |
| Reference:
|
[S1] Sato, R.: A remark on the ergodic Hilbert transform.Math. J. Okayama Univ. 28 (1986), 159–163. Zbl 0641.47008, MR 0885025 |
| Reference:
|
[S2] Sato, R.: On pointwise ergodic theorems for positive operators.Studia Math. 97 (1990), 71–84. Zbl 0755.47005, MR 1083338 |
| Reference:
|
[S3] Sato, R.: Pointwise ergodic theorems for functions in Lorentz spaces $L_{pq}$ with $p\ne \infty $.Studia Math. 109 (1994), 209–216. MR 1269777 |
| Reference:
|
[Sa] Sawyer, E.: Weighted inequalities for the one sided Hardy-Littlewood maximal functions.Trans. Amer. Math. Soc. 297 (1986), 53–61. Zbl 0627.42009, MR 0849466 |
| Reference:
|
[T] Torchinsky, A.: Real Variable Methods in Harmonic Analysis.Academic Press, Inc., 1986. Zbl 0621.42001, MR 0869816 |
| Reference:
|
[W] Wiener, N.: The ergodic theorem.Duke Math. J. 5 (1939), 1–18. Zbl 0021.23501, MR 1546100 |
| . |
