- 期刊
FOURIER SERIES AND THE MAXIMAL OPERATOR ON THE WEIGHTED SPECIAL ATOM SPACES
摘要
For an interval I in [0, 2π] with halves L and R, a weighted special atom looks like b(t) = 1/p(|I|) [X_L(t) - X_R(t)], where p is a non-ngative function satisfying some properties. We consider the weighted special atom space B(p) formed by I^1 linear combinations of these weighted atoms. We showed that if f ε B(p) then its Fourier series converges almost everywhere, using the Carleson-Hunt idea on their famous result about the almost everywhere convergence on L_P-spaces.
延伸閱讀
- Muminov, Z., Ismail, F., Eshkuvatov, Z., & Rasulov, J. (2013). On the Discrete Spectrum of a Model Operator in Fermionic Fock Space. Abstract and Applied Analysis, 2013(), 144-155-1212. https://doi.org/10.1155/2013/875194
- Nigam, H. K., & Sharma, A. (2009). On (N, p, q)(E, 1) Summability of Fourier Series. International Journal of Mathematics and Mathematical Sciences, 2009(), 1271-1278. https://doi.org/10.1155/2009/989865
- Souza, G. S. D. (1984). RESEARCH NOTES ON THE CONVERGENCE OF FOURIER SERIES. International Journal of Mathematics and Mathematical Sciences, 1984(), 817-820. https://doi.org/10.1155/S0161171284000843
- Hashemiparast, S. M., & Fallahgoul, H. (2009). Fourier Approximation for Integral Equations on the Real Line. Mathematical Problems in Engineering, 2009(), 862-871-150. https://doi.org/10.1155/2009/786368
- Mishra, K. N., & Srivastava, R. S. L. (1985). ON THE STRONG MATRIX SUMMABILITY OF DERIVED FOURIER SERIES. International Journal of Mathematics and Mathematical Sciences, 1985(), 367-372. https://doi.org/10.1155/S0161171285000382