DOI:
https://doi.org/10.69717/ijams.v2.i2.141Keywords:
Complex interpolation, Lorentz space, Real interpolation, Herz space, Herz- type Triebel-Lizorkin space, Herz-type Besov space, Maximal inequalities, Sobolev embeddingsAbstract
Communicated Editor: A. Chala.
Manuscript received August. 01st, 2025; revised November 02, 2025; accepted November 06, 2025; published November 11, 2025.
Downloads
References
Bhat, M. A., Kolwicz, P., & Kosuru, G. (2022). K" othe-Herz Spaces: The Amalgam-Type Spaces of Infinite Direct Sums. arXiv preprint arXiv:2209.05897. PDF.
Baernstein, I. I. (1985). A., Sawyer, ET: Embedding and multiplier theorems for Hp (Rn). Mem. Amer. Math. Soc, 318, 1-82. Google Scholar
Bergh, J. (1976). J. L ofstr om, Interpolation Spaces. An Introduction,’’Springer, Berlin. Google Scholar.
Beurling, A. (1964). Construction and analysis of some convolution algebras. In Annales de l'institut Fourier (Vol. 14, No. 2, pp. 1-32). Google scholar. https://doi.org/10.5802/aif.172
Brezis, H., & Mironescu, P. (2001). Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces. Journal of Evolution Equations, 1(4), 387-404.Google Scholar. https://dx.doi.org/10.1007/PL00001378
Qui, B. H. (1982). Weighted Besov and Triebel spaces: Interpolation by the real method. Hiroshima Mathematical Journal, 12(3), 581-605. Google Scholar. PDF
Drihem, D. (2013). Embeddings properties on Herz-type Besov and Triebel-Lizorkin spaces. Math. Inequal. Appl, 16(2), 439-460. Google Scholar. http://dx.doi.org/10.7153/mia-16-32
Drihem, D. (2017). Sobolev embeddings for Herz-type Triebel-Lizorkin spaces. In Function Spaces and Inequalities: New Delhi, India, December 2015 (pp. 15-35). Singapore: Springer Singapore. Google Scholar. https://doi.org/10.1007/978-981-10-6119-6_2.
Drihem, D. (2018). Complex interpolation of Herz‐type Triebel–Lizorkin spaces. Mathematische Nachrichten, 291(13), 2008-2023. Google Scholar. https://doi.org/10.1002/mana.201700266.
Drihem, D. (2020). Herz-Sobolev spaces on domains. arXiv preprint arXiv:2004.05445. Google Scholar.
Drihem, D. (2022). Composition operators on Herz-type Triebel–Lizorkin spaces with application to semilinear parabolic equations. Banach Journal of Mathematical Analysis, 16(2), 29. Google Scholar. https://doi.org/10.1007/s43037-022-00178-6.
Drihem, D. (2023). Semilinear parabolic equations in Herz spaces. Applicable Analysis, 102(11), 3043-3063. Google Scholar. https://doi.org/10.1080/00036811.2022.2047948.
Drihem, D. (2025). Lorentz Herz-type Besov and Triebel-Lizorkin spaces, Advances in Operator Theory, 10 )75(, 117 pp.https://doi.org/10.1007/s43036-025-00463-9
Feightinger, H. G. (1984). An elementary approach to Wiener’s third Tauberian Theorem for the Euclidean n− spaces. In Proceedings of Conference at Cortona (pp. 267-301).Google Scholar.
Feichtinger, H. G., & Weisz, F. (2008). Herz spaces and summability of Fourier transforms. Mathematische Nachrichten, 281(3), 309-324. Google Scholar. https://doi.org/10.1002/mana.200510604.
Grafakos, L. (2008). Classical fourier analysis (Vol. 2). New York: Springer. Google Scholar. PDF.
Herz, C. S. (1968). Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transforms. Journal of Mathematics and Mechanics, 18(4), 283-323. Google Scholar. View.
Hernández, E., & Yang, D. (1998). Interpolation of Herz-type Hardy spaces. Illinois Journal of Mathematics, 42(4), 564-581. Google Scholar. DOI: 10.1215/ijm/1255985461.
Ho, K. P. (2008). Remarks on Littlewood–Paley analysis. Canadian Journal of Mathematics, 60(6), 1283-1305. Google Scholar. https://doi.org/10.4153/CJM-2008-055-x.
Ho, K. P. (2011). Littlewood-Paley spaces. Mathematica Scandinavica, 77-102. Google Scholar. View
Ho, K. P. (2018). Young’s inequalities and Hausdorff–Young inequalities on Herz spaces. Bollettino dell'Unione Matematica Italiana, 11(4), 469-481. Google Scholar. https://doi.org/10.1007/s40574-017-0147-8.
Li, X., & Yang, D. (1996). Boundedness of some sublinear operators on Herz spaces. Illinois Journal of Mathematics, 40(3), 484-501. Google Scholar. PDF.
Lu, S., & Yang, D. (1997). Herz-type Sobolev and Bessel potential spaces and their applications. Science in China Series A: Mathematics, 40(2), 113-129. Google Scholar. https://doi.org/10.1007/BF02874431.
Lu, S., Yang, D., & Hu, G. (2008). Herz type spaces and their applications (pp. 131-132). Beijing: Science Press. Google Scholar.
Meyries, M ., Veraar, M. C. (2012). Sharp embedding results for spaces of smooth functions with power
weights, Studia. Math. 208(3), 257–293. DOI: 10.4064/sm208-3-5
Rafeiro, H., & Samko, S. (2020). Herz spaces meet Morrey type spaces and complementary Morrey type spaces. Journal of Fourier Analysis and Applications, 26(5), 74. Google Scholar. https://doi.org/10.1007/s00041-020-09778-y.
Ragusa, M. A. (2009). Homogeneous Herz spaces and regularity results. Nonlinear Analysis: Theory, Methods & Applications, 71(12), e1909-e1914. Google Scholar. https://doi.org/10.1016/j.na.2009.02.075.
Ragusa, M. A. (2012). Parabolic Herz spaces and their applications. Applied Mathematics Letters, 25(10), 1270-1273. Google Scholar. https://doi.org/10.1016/j.aml.2011.11.022.
Seeger, A., & Trebels, W. (2019). Embeddings for spaces of Lorentz–Sobolev type. Mathematische Annalen, 373(3), 1017-1056. Google Scholar. https://doi.org/10.1007/s00208-018-1730-8.
Sickel, W., Skrzypczak, L., & Vybíral, J. (2014). Complex interpolation of weighted Besov and Lizorkin-Triebel spaces. Acta Mathematica Sinica, English Series, 30(8), 1297-1323. Google Scholar. https://doi.org/10.1007/s10114-014-2762-y.
Lin, T., & Dachun, Y. (2000). Boundedness of vector-valued operators on weighted Herz spaces. Approximation Theory and its Applications, 16(2), 58-70.Google Scholar. https://doi.org/10.1007/BF02837394.
Triebel, H. (1995). Interpolation theory, function spaces, differential operators. JA Barth. Google Scholar. Article
Triebel, H. (1983). Theory of function spaces, Birkhauser, Basel. Google Scholar.
Triebel, H. (2006). Theory of function spaces III. Basel: Birkhäuser Basel.Google Scholar. https://doi.org/10.1007/3-7643-7582-5_1.
Tsutsui, Y. (2011). The Navier-Stokes equations and weak Herz spaces. Google Scholar. https://doi.org/10.57262/ade/1355703112.
Xu, J. S., & Yang, D. C. (2005). Herz-type Triebel–Lizorkin Spaces, I. Acta Mathematica Sinica, 21(3), 643-654. Google Scholar. https://doi.org/10.1007/s10114-004-0424-1.
Xu, J. (2005). Equivalent norms of Herz‐type Besov and Triebel‐Lizorkin spaces. Journal of Function Spaces, 3(1), 17-31. Google Scholar. https://doi.org/10.1155/2005/149703.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 International Journal of Applied Mathematics and Simulation
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.