Abstract
B-maximal functions in \(HM^p_{q,{\varDelta _{\nu }}}\) Hardy–Morrey spaces, related to a Laplace–Bessel differential operator, are studied. We give B-maximal characterization of \(HM^p_{q,{\varDelta _{\nu }}}\) Hardy–Morrey spaces and study the atomic decomposition theory which has the same cancellation properties of the \(H^{p}_{\varDelta _{\nu }}({\mathbb {R}}^{n}_{+})\) Hardy spaces.
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References
Akbulut, A., Guliyev, V.S., Noi, T., Sawano, Y.: Generalized Hardy–Morrey spaces. Z. Anal. Anwend. 36(2), 129–149 (2017)
Aliev, I.A.: On Riesz transformations generated by a generalized shift operator. Ivestiya Acad. Sci. Azerbaydian 1, 7–13 (1987)
Ekincioglu, I., Keskin, C., Guliyev, R.V.: Lipschitz estimates for rough fractional multilinear integral operators on local generalized Morrey spaces. Tbilisi Math. J. 13(1), 47–60 (2020)
Ekincioglu, I., Keskin, C., Serbetci, A.: Multilinear commutators of Calderón–Zygmund operator on generalized variable exponent Morrey spaces. Positivity 25(4), 1551–1567 (2021)
Ekincioglu, I., Shishkina, E.L., Kaya, E.: On the boundedness of the generalized translation operator on variable exponent Lebesgue spaces. Acta Appl. Math 173(4), 14 (2021)
Grafakos, L.: Modern Fourier Analysis. Graduate Texts in Mathematics. Springer, New York (2008)
Guliyev, V.S.: On maximal function and fractional integral associated with the Bessel differential operator. Math. Inequal. Appl. 6(2), 317–330 (2003)
Guliyev, V.S., Hasanov, S.G., Sawano, Y.: Decompositions of local Morrey-type spaces. Positivity 21(3), 1223–1252 (2017)
Ho, K.: Atomic decompositions of weighted Hardy–Morrey spaces. Hokkaido Math. J. 42, 131–157 (2013)
Ho, K.: Atomic decomposition of Hardy–Morrey spaces with variable exponents. Ann. Acad. Sci. Fenn. Math. 40(1), 31–62 (2015)
Iida, T., Sawano, Y., Tanaka, H.: Atomic decomposition for Morrey spaces. Z. Anal. Anwend. 33(2), 149–170 (2014)
Jia, H., Wang, H.: Decomposition of Hardy–Morrey spaces. J. Math. Anal. Appl. 354(1), 99–110 (2009)
Jia, H., Wang, H.: Singular integral operator, Hardy–Morrey space estimates for multilinear operators and Navier–Stokes equations. Math. Methods Appl. Sci 33, 1661–1684 (2010)
Keskin, C., Ekincioglu, I., Guliyev, V.S.: Characterizations of Hardy spaces associated with Laplace–Bessel operators. Anal. Math. Phys. 19(4), 2281–2310 (2019)
Levitan, B.M.: Bessel function expansions in series and Fourier integrals. Uspekhi Mat. Nauk. 6(2), 102–143 (1951). (Russian)
Lyakhov, L.N.: Multipliers of the mixed Fourier–Bessel transform. Proc. Steklov Inst. Math. 214, 234–249 (1997)
Sawano, Y.: Atomic decompositions of Hardy spaces with variable exponents and its application to bounded linear operators. Integr. Equ. Oper. Theory 77(1), 123–148 (2013)
Acknowledgements
The authors would like to thank the reviewers for valuable suggestions and corrections. The research of C. Keskin was supported by the grant of Cooperation Program 2532 TUBITAK-RFBR (Russian foundation for basic research) with agreement No. 119N455.
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Keskin, C. Different approach to the decomposition theory of \(HM^p_{q,{\varDelta _{\nu }}}\) Hardy–Morrey spaces. J. Pseudo-Differ. Oper. Appl. 12, 54 (2021). https://doi.org/10.1007/s11868-021-00426-7
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DOI: https://doi.org/10.1007/s11868-021-00426-7