Convergence in Measure of Logarithmic Means of Quadratical Partial Sums of Double Walsh-Kaczmarz-Fourier Series
The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz series does not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of L log+ L(I2), the set of the functions the log...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/582726 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832566836969865216 |
|---|---|
| author | Ushangi Goginava Károly Nagy |
| author_facet | Ushangi Goginava Károly Nagy |
| author_sort | Ushangi Goginava |
| collection | DOAJ |
| description | The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz series does not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of L log+ L(I2), the set of the functions the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz series of which converge in measure is of first Baire category. |
| format | Article |
| id | doaj-art-891cd900762c4dbb8aea5d858402ff54 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-891cd900762c4dbb8aea5d858402ff542025-02-03T01:03:03ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/582726582726Convergence in Measure of Logarithmic Means of Quadratical Partial Sums of Double Walsh-Kaczmarz-Fourier SeriesUshangi Goginava0Károly Nagy1Institute of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, Chavchavadze Street 1, 0128 Tbilisi, GeorgiaInstitute of Mathematics and Computer Sciences, College of Nyíregyháza, P.O. Box 166, Nyíregyháza 4400, HungaryThe main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz series does not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of L log+ L(I2), the set of the functions the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz series of which converge in measure is of first Baire category.http://dx.doi.org/10.1155/2012/582726 |
| spellingShingle | Ushangi Goginava Károly Nagy Convergence in Measure of Logarithmic Means of Quadratical Partial Sums of Double Walsh-Kaczmarz-Fourier Series Journal of Function Spaces and Applications |
| title | Convergence in Measure of Logarithmic Means of Quadratical Partial Sums of Double Walsh-Kaczmarz-Fourier Series |
| title_full | Convergence in Measure of Logarithmic Means of Quadratical Partial Sums of Double Walsh-Kaczmarz-Fourier Series |
| title_fullStr | Convergence in Measure of Logarithmic Means of Quadratical Partial Sums of Double Walsh-Kaczmarz-Fourier Series |
| title_full_unstemmed | Convergence in Measure of Logarithmic Means of Quadratical Partial Sums of Double Walsh-Kaczmarz-Fourier Series |
| title_short | Convergence in Measure of Logarithmic Means of Quadratical Partial Sums of Double Walsh-Kaczmarz-Fourier Series |
| title_sort | convergence in measure of logarithmic means of quadratical partial sums of double walsh kaczmarz fourier series |
| url | http://dx.doi.org/10.1155/2012/582726 |
| work_keys_str_mv | AT ushangigoginava convergenceinmeasureoflogarithmicmeansofquadraticalpartialsumsofdoublewalshkaczmarzfourierseries AT karolynagy convergenceinmeasureoflogarithmicmeansofquadraticalpartialsumsofdoublewalshkaczmarzfourierseries |