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The amalgam space L(p,q)π(G) on IN-groups

  • Fatemeh Abtahi , Ali Rejali and Navid Sabzali
Published/Copyright: January 13, 2020
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 70 Issue 1

Abstract

Let G be an IN-group and 0 < p, q < ∞. In this paper, we determine necessary and sufficient conditions for the existence of the convolution of functions, in the amalgam space L(p,q)π(G).

Keywords: Amalgam space; convolution; IN-group
MSC 2010: Primary 43A15; Secondary 43A20

  1. Communicated by Gregor Dolinar

References

[1] Abtahi, F.—Nasr Isfahani, R.—Rejali, A.: On the Lp-conjecture for locally compact groups, Arch. Math. (Basel) 89, (2007), 237–242.10.1007/s00013-007-1993-xSearch in Google Scholar

[2] Abtahi, F.—Nasr Isfahani, R.—Rejali, A.: On the weighted Lp-space on a discrete group, Publ. Math. Debrecen 75(3–4) (2009), 365–374.10.5486/PMD.2009.4372Search in Google Scholar

[3] Abtahi, F.: Weighted Lp-spaces on locally compact groups Bull. Belg. Math. Soc. Simon Stevin 19(2) (2012), 339–343.10.36045/bbms/1337864277Search in Google Scholar

[4] Abtahi, F.—Nasr Isfahani, R.—Rejali, A.: Convolution on Lp-space of a locally compact group, Math. Slovaca 63(2) (2013), 291–298.10.2478/s12175-012-0098-6Search in Google Scholar

[5] Bertrandias, J. P.—Darty, C.—Dupuis, C.: Unions et intersections ’ espace LP invariantes partransation ou convolution, Ann. Ins. Fourier (Grenoble). 28 (1978), 58–84.Search in Google Scholar

[6] Busby, R. C.—Smith, H. A.: Product-convolution operators and mixed-norm spaces, Trans. Amer. Math. Soc. 263 (1981), 309–341.10.1090/S0002-9947-1981-0594411-4Search in Google Scholar

[7] Feichtinger, H. G.: On a new Segal algebra, Monatsh. Math. 92 (1981), 269–289.10.1007/BF01320058Search in Google Scholar

[8] Feichtinger, H. G.: Banach convolution algebras of Wiener type, Proc. Conf. on Functions, Series, Operators, Budapest 1980, Colloq. Math. Soc. Janos Bolyai. 35 (1983), 509–524.Search in Google Scholar

[9] Guo, W.—Fan, D.—Wu, H.—Zhao, G.: Sharp weighted convolution inequalities and some applications, Studia Math. 241(3) (2018), 201–239.10.4064/sm8583-5-2017Search in Google Scholar

[10] Hewitt, E.—Ross, K.: Abstract Harmonic Analysis I, Springer-Verlag, New York, 1970.10.1007/978-3-662-26755-4Search in Google Scholar

[11] Holland, F.: Harmonic analysis on amalgams of Lp and lq, J. London Math. Soc. 10 (1975), 295–305.10.1112/jlms/s2-10.3.295Search in Google Scholar

[12] Saeki, S.: The Lp-conjecture and Young’s inequality, Illinois J. Math. 34 (1990), 615–627.10.1215/ijm/1255988174Search in Google Scholar

[13] Stewart, J.: Fourier transform of unbounded measure, Canad. J. Math. 31 (1979), 1281–1292.10.4153/CJM-1979-106-4Search in Google Scholar

[14] Stewart, J.—Watson, S.: Which amalgams are convolution algebras?, Proc. Amer. Math. Soc. 93 (1985), 621–627.10.1090/S0002-9939-1985-0776191-1Search in Google Scholar

[15] Torres, M.: Amalgams of Lp and ℓq, PHD Thesis, Mc Master University, USA, 1984.Search in Google Scholar

[16] Wiener, N.: On the representation of functions by trigonometric integrals, Math. Z. 24 (1926), 575–616.10.1007/BF01216799Search in Google Scholar

[17] Zelazko, W.: A theorem on the discrete groups and algebras Lp, Colloq. Math. 8 (1961), 205–207.10.4064/cm-8-2-205-207Search in Google Scholar

[18] Zelazko, W.: On the algebras Lp of a locally compact group, Colloq. Math. 8 (1961), 112–120.Search in Google Scholar
Received: 2018-09-27
Accepted: 2019-06-25
Published Online: 2020-01-13
Published in Print: 2020-02-25

© 2020 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0337
Keywords for this article
Amalgam space; convolution; IN-group

Articles in the same Issue

  1. Regular papers
  2. Doc. RNDr. Roman Frič, DrSc. – 3/4 C?
  3. Sugihara algebras and Sugihara monoids: Multisorted dualities
  4. Two by two squares in set partitions
  5. Identifying quantum logics by numerical events
  6. Some remarks on divisible polyhedral MV-algebras
  7. Remarks on b-metrics, ultrametrics, and metric-preserving functions
  8. Estimates of essential norm of generalized weighted composition operators from Bloch type spaces to nth weighted type spaces
  9. Maximum term of transcendental entire function and spider’s web
  10. Entire solutions of certain type of non-linear differential equations
  11. On the oscillatory behavior of third order differential equations with a sublinear neutral term
  12. Eigenvalue problems for a class of nonlinear Hadamard fractional differential equations with p-Laplacian operator
  13. The amalgam space L(p,q)π(G) on IN-groups
  14. On the topology of partial metric spaces
  15. The trace of the commutator of the Cesàro operator and a compact operator
  16. Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold
  17. On 4-th root metrics of isotropic scalar curvature
  18. On ultrametric-preserving functions
  19. Porosity of 𝓢-approximately continuous functions
  20. On a modified Burr XII distribution having flexible hazard rate shapes
  21. A study of chi-square-type distribution with geometrically distributed degrees of freedom in relation to distributions of geometric random sums
  22. An alternative estimate for the numerical radius of Hilbert space operators
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