Approximation of $$\tilde{f},$$f~, conjugate function of f belonging to a subclass of $$L^{p}$$Lp-space, by product means of conjugate Fourier series

Abstract

The deviation of $$\tilde{f},$$ conjugate function of f, by various summability means of its conjugate Fourier series has been of growing interest of researchers. Recently, the authors (W. Lenski and B. Szal, 47(4):878–892 (2014)) have estimated the pointwise deviation of $$\tilde{f}$$ in terms of modulus of continuity in $$L^{p}$$-space by product means. In this paper, we obtained the deviation of $$\tilde{f},$$ conjugate function of f belonging to a subclass of $$L^{p}(p\ge 1)$$-space, with less assumption conditions on the product matrix. We introduce different conditions on the modulus of continuity. We also discuss the case for $$p=1$$ separately. Our results are free from p.