Denote by $f_{\rm ss}(x,y)$ the sum of a double sine series with nonnegative coefficients. We present necessary and sufficient coefficient conditions in order that ss}$ belongs to two-dimensional multiplicative Lipschitz class ${\rm Lip}(\alph

We study the smoothness properties of a complex-valued function

For a Lebesgue integrable complex-valued function f defined on R , let be its Fourier transform.The Riemann-Lebesgue lemma says that (t) → 0 as |t| ∞ .But in general, there is no definite rate at which the transform tends to zero.In fact, of an can tend zero slowly we wish.Therefore, it interesting know for functions subclasses L 1 (R) this paper, determine bounded variation .We also such sense Vitali N (N ∈ N) .

Mindannyian tapasztaljuk, hogy a hallgatók figyelmét megragadni szinte már csak vizuális ingerekkel lehet. Mindezek mellett mesterséges intelligencia térnyerésével jelentősen felerősödött „Minek ez?” hozzáállás is. Sajnos, vagy nem, nekünk kell alkalmazkodni. Amennyire lehet, látványossá tenni az óránkat, élményt adni, úgy, közben hallgató használható ismeretekkel gyarapodjon, absztrakciós készsége fejlődjön. Ebben cikkben bemutatjuk, matematika bevezető tárgyainak oktatásával kapcsolatban...

For a Lebesgue integrable complex-valued function f defined on R + := [0, ∞) let be its Walsh-Fourier transform.The Riemann-Lebesgue lemma says that (y) → 0 as y ∞.But in general, there is no definite rate at which the transform tends to zero.In fact, of an can tend zero slowly we wish.Therefore, it interesting know for functions subclasses L 1 (R ) zero.We determine this bounded variation .We also such sense Vitali N , ∈ N.

We investigate the pointwise and uniform convergence of symmetric rectangular partial (also called Dirichlet) integrals double Fourier integral a function that is Lebesgue integrable bounded variation over ℝ 2 . Our theorem two-dimensional extension Móricz (see Theorem 3 in [10]) concerning single integrals, which more general than given by himself [11]).

In this study the definition of bounded variation order p (p ∈ ℕ) for double sequences is considered. Some inclusion relations are proved and counter examples provided ensuring proper inclusions.