en تخصصي Special پژوهشي Research paper <div style="text-align: justify;">In this paper we characterize Fredholm and invertible composition operators on harmonic Bloch function spaces. Indeed, we provide some necessary and sufficient conditions for Fredholmness of composition operators. Also, we investigate the relation between the Fredholm and invertible composition operators on harmonic Bloch function spaces.</div> Harmonic function, Fredholm operator, Composition operator, Univalent function. 31 39 http://ijmsi.ir/browse.php?a_code=A-10-1292-1&slc_lang=en&sid=1 Y. Estaremi yestaremi@gu.ac.ir 100319475328460011676 100319475328460011676 Yes Department of Mathematics and Computer Sciences, Golestan University, Gorgan, Iran A. Ebadian ebadian.ali@gmail.com 100319475328460011677 100319475328460011677 No Department of Mathematics, Urmia University, Urmia, Iran S. Esmaeili dr.somaye.esmaili@gmail.com 100319475328460011678 100319475328460011678 No Department of Mathematics, Payame Noor University, P. O. Box: 19395-3697, Tehran, Iran