Pratima Sadangi in a Ph.D. thesis submitted to Utkal University proved results on degree of approximation of functions by operators associated with their Fourier series. In this dissertation, we consider degree of approximation of functions in Hα,ρ by different operators. In Chapter 1 we mention basic definitions needed for our work. In Chapter 2 we discuss different methods of summation. In Chapter 3 we define the Hα,ρ metric and present the degree of approximation problem relating to Fourier series and conjugate series of functions in the Hα,ρ metric using Karamata (Κλ) means. In Chapter 4 we present the degree of approximation of an integral associated with the conjugate series by the Euler, Borel and (e,c) means of a series analogous to the Hardy-Littlewood series in the Hα,ρ metric. In Chapter 5 we propose problems to be solved in the future.