**Title:** Bilinear multipliers theory on some function spaces

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-22-00033; **Volume 5 / Issue 3 / Year 2023**, Pages 95-104

**Document Type:** Research Paper

**Author(s):** Hüseyin Çakır ^{a} , Öznur Kulak ^{b}

^{a}Department of Mathematics, Institute of Sciences, Amasya University, Amasya, Turkey

^{b}Department of Mathematics, Faculty of Arts and Sciences, Amasya University, Amasya, Turkey

Received:2 November 2022, Accepted:12 January 2023, Published:13 February 2023.

**Corresponding Author:** Öznur Kulak (Email address: oznur.kulak@amasya.edu.tr)

**Full Text:** PDF

**Abstract**

In this work, we define the bilinear multipliers of the spaces with fractional wavelet transform and consider the basic properties of these bilinear multipliers. Moreover, we give construction examples of bilinear multipliers.

**Keywords:** Bilinear multipliers, fractional wavelet transform, weighted Lebesgue spaces

**References:**

- O. Blasco,
*Notes on the spaces of bilinear multipliers*, Rev. Un. Mat. Argentina**50 (2)**, 23–37, 2009. - I. Daubechies,
*Ten lectures on wavelets*, CBMS-NSF, SIAM, Philadelphia, 1992. - M. Duman and Ö. Kulak,
*On function spaces with fractional wavelet transform*, Montes Taurus J. Pure Appl. Math.**3 (3)**, 122–134, 2021. - C. Gasquet and P. Witomski,
*Fourier analysis and applications*, Springer, New York, 1999. - A. T. Gürkanlı, Ö. Kulak and A. Sandıkçı,
*The spaces of bilinear multipliers of weighted Lorentz type modulation spaces*, Georgian Math. J.**23 (3)**, 351–362, 2016. - Ö. Kulak,
*Bilinear multipliers of function spaces with wavelet transform in*, Proc. Jangjeon Math. Soc.*L*_{ω}^{p}(ℝ^{n})**20 (1)**, 81–94, 2017. - Ö. Kulak and A. T. Gürkanli,
*Bilinear multipliers of weighted Lebesgue spaces and variable exponent Lebesgue spaces*, J. Inequal. Appl.**2013**, 2013; Article ID: 259. - Ö. Kulak and A. T. Gürkanli,
*Bilinear multipliers of weighted Wiener amalgam spaces and variable exponent Wiener amalgam spaces*, J. Inequal. Appl.**2014**, 2014; Article ID: 476. - Ö. Kulak and A. T. Gürkanli,
*Bilinear Multipliers of weighted Lorentz spaces and variable exponent Lorentz spaces*, Mathematics and Statistics,**5 (1)**, 5–18, 2017. - Ö. Kulak and A. T. Gürkanli,
*Bilinear multipliers of small Lebesgue spaces*, Turkish J. Math.**45 (5)**, 1959–1984, 2021. - A. Prasad, S. Manna, A. Mahato and V. K. Singh,
*The generalized continuous wavelet transform associated with the fractional Fourier transform*, J. Comput. Appl. Math.**259**, 660–671, 2014. - A. Prasad and P. Kumar,
*Fractional wavelet transform in terms of fractional convolution*, Progr. Fract. Differ. Appl.**3**, 201–210, 2015. - W. Rudin,
*Fourier analysis on groups*, Interscience, New York, 1962. - A. Sandıkçı and E. Toksoy,
*On an abstract Segal algebra under fractional convolution*, Montes Taurus J. Pure Appl. Math.**4 (1)**, 1–22, 2022. - E. Toksoy and A. Sandıkçı,
*On function spaces with fractional Fourier transform in weighted Lebesgue spaces*, J. Inequal. Appl.**2015**, 2015; Article ID: 87. - E. Toksoy and A. Sandıkçı,
*Some compact and non-compact embedding theorems for the function spaces defined by fractional Fourier transform*, Hacet. J. Math. Stat.**50 (6)**, 1620–1635, 2021.