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 Slant H-Toeplitz Operators on the Hardy space J. Korean Math. Soc.Published online 2019 Feb 12 Anuradha Gupta, and Shivam kumar Singh Department of Mathematics, Delhi College of arts and commerce, University of Delhi, Delhi, Department of Mathematics, University of Delhi, Delhi Abstract : The notion of slant H-Toeplitz operator $V_\phi$ on the Hardy space $H^2$ is introduced and its characterizations are obtained. It has been shown that an operator on the space $H^2$ is slant H-Toeplitz if and only if its matrix is a slant H-Toeplitz matrix. In addition, the conditions under which slant Toeplitz and slant Hankel operators become slant H-Toeplitz operators are also obtained. Keywords : Toeplitz operator, Hankel operator, Slant Toeplitz operator, Slant Hankel operator, H-Toeplitz operator MSC numbers : Primary 47B35; Secondary 47B32 Full-Text :