Functions of generalized bounded variation and its multiple fourier coefficients
Copyright policy )Functions of generalized bounded variation and its multiple fourier coefficients
Summary: Here, generalizing the class \((\Lambda^1,\Lambda^2)^{\ast} BV^{(p)}([0,2\pi]^2)\) to the class \((\Lambda^1,\Lambda^2)^{\ast} BV^{(p,q)}([0,2\pi]^2)\) of functions of \(p,q\)-\((\Lambda^1,\Lambda^2)^{\ast}\)-bounded variation, it is observed that the class is a Banach space with respect to the pointwise operations and the generalized variation norm. Moreover, we estimate the order of magnitude of multiple Fourier coefficients of a function of this class.
Normed linear spaces and Banach spaces; Banach lattices, Fourier coefficients, Fourier series of functions with special properties, special Fourier series, Banach space, Fourier series and coefficients in several variables, functions of generalized bounded variation, Functions of bounded variation, generalizations, Inequalities for sums, series and integrals, order of magnitude of multiple Fourier coefficients
Normed linear spaces and Banach spaces; Banach lattices, Fourier coefficients, Fourier series of functions with special properties, special Fourier series, Banach space, Fourier series and coefficients in several variables, functions of generalized bounded variation, Functions of bounded variation, generalizations, Inequalities for sums, series and integrals, order of magnitude of multiple Fourier coefficients
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