Where ever there is a dot product, the kernel trick can be implemented. actually I implement it on Pearson correlation. for testing, I generated two random signals, the correlation coefficient is very low ... after implementing the kernel method, the correlation coefficient must be very low again (because they are random signals and there is no correlation between them) but the result show high correlation coefficient.
This is tricky. Generally, you can hardly implement the kernel trick for Pearson correlation. Note, that Pearson correlation is mean-shifted, that is, first the means of the vectors need to be subtracted in the feature space. With the Gaussian kernel, the feature space is infinite dimensional... what you might have implemented is simple correlation, which is the normalized inner product: k(x,y)/sqrt(k(x,x)*k(y,y)).
The result highly depends on the scale (variance) parameter of the Gaussian kernel. Note that the denominator becomes to 1, thus, the smaller variance parameter you use compared to the range of your vector coordinates, the larger result you get.
Eventually, I have a paper on this, (how to compute the Pearson correlation in kernel space) and the second chapter of thesis contains a more clarified description, you might find it interesting:
Article Translation Invariance in the Polynomial Kernel Space and It...
Thesis Advances in the theory and applications of (dis)similarity f...
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