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 $k^{th}$-order Essentially Slant Weighted Toeplitz Operators Commun. Korean Math. Soc.Published online March 12, 2019 Anuradha Gupta and Shivam kumar Singh Associate Professor, Department of Mathematics, Delhi college of Arts and Commerce, Univerity of Delhi, Delhi, India, Department of Mathematics, University of Delhi, Delhi, India Abstract : The notion of $k^{th}$-order essentially slant weighted Toeplitz operator on the weighted Lebesgue space $L^2(\beta)$ is introduced and its algebraic properties are investigated. In addition, the compression of $k^{th}$-order essentially slant weighted Toeplitz operators on the weighted Hardy space $H^2(\beta)$ is also studied. Keywords : Weighted Toeplitz operators, $k^{th}$-order slant Toeplitz operators, $k^{th}$-order essentially slant weighted Toeplitz operators, Fredholm operators MSC numbers : MSC Primary 47B35, Secondary 47B38 Full-Text :